Package 'distrMod'

Title: Object Oriented Implementation of Probability Models
Description: Implements S4 classes for probability models based on packages 'distr' and 'distrEx'.
Authors: Matthias Kohl [aut, cph], Peter Ruckdeschel [cre, cph], R Core Team [ctb, cph] (for source file 'format.perc')
Maintainer: Peter Ruckdeschel <[email protected]>
License: LGPL-3
Version: 2.9.6
Built: 2024-10-24 02:22:05 UTC
Source: https://github.com/r-forge/distr

Help Index


distrMod – Object Oriented Implementation of Probability Models

Description

Based on the packages distr and distrEx package distrMod provides a flexible framework which allows computation of estimators like maximum likelihood or minimum distance estimators for probability models.

Details

Package: distrMod
Version: 2.9.6
Date: 2024-10-23
Depends: R(>= 3.4), distr(>= 2.8.0), distrEx(>= 2.8.0), RandVar(>= 1.2.0), MASS, stats4,methods
Imports: startupmsg, sfsmisc, graphics, stats, grDevices
Suggests: ismev, evd,
Enhances: RobExtremes
ByteCompile: yes
License: LGPL-3
URL: https://distr.r-forge.r-project.org/
VCS/SVNRevision: 1478

Classes

[*]: there is a generating function with the same name
##########################
ProbFamily classes
##########################
slots: [<name>(<class>)]
name(character), distribution(Distribution),
distrSym(DistributionSymmetry), props(character)
"ProbFamily"
|>"ParamFamily"     [*]
additional slots:
param(ParamFamParameter), modifyParam(function),
startPar(function), makeOKPar(function), fam.call(call)
|>|>"L2ParamFamily" [*]
additional slots:
L2deriv(EuclRandVarList), L2deriv.fct(function),
L2derivSymm(FunSymmList), L2derivDistr(DistrList),
L2derivDistrSymm(DistrSymmList), FisherInfo(PosSemDefSymmMatrix),
FisherInfo.fct(function)
|>|>|>"BinomFamily" [*]
|>|>|>"PoisFamily"  [*]
|>|>|>"BetaFamily"  [*]
|>|>|>"NbinomFamily" [*]
|>|>|>"NbinomwithSizeFamily" [*]
|>|>|>"NbinomMeanSizeFamily" [*]
|>|>|>"L2GroupParamFamily"
additional slots:
LogDeriv(function)
|>|>|>|>"L2ScaleShapeUnion"  /VIRTUAL/
|>|>|>|>|>"GammaFamily" [*]
|>|>|>|>"L2LocationScaleUnion"  /VIRTUAL/
additional slots:
locscalename(character)
|>|>|>|>|>"L2LocationFamily"              [*]
|>|>|>|>|>|>"NormLocationFamily"          [*]
|>|>|>|>|>"L2ScaleFamily"                 [*]
|>|>|>|>|>|>"NormScaleFamily"             [*]
|>|>|>|>|>|>"ExpScaleFamily"              [*]
|>|>|>|>|>|>"LnormScaleFamily"            [*]
|>|>|>|>|>"L2LocationScaleFamily"         [*]
|>|>|>|>|>|>"NormLocationScaleFamily"     [*]
|>|>|>|>|>|>"CauchyLocationScaleFamily"   [*]
|>|>|>|>|>|>"LogisticLocationScaleFamily" [*]
and a (virtual) class union "L2ScaleUnion"  between
   "L2LocationScaleUnion"  and "L2ScaleShapeUnion"
##########################
ParamFamParameter
##########################
"ParamFamParameter" [*] is subclass of class "Parameter" of package "distr".
Additional slots:
main(numeric), nuisance(OptionalNumeric), fixed(OptionalNumeric),
trafo(MatrixorFunction)
##########################
Class unions
##########################
"MatrixorFunction" = union("matrix", "OptionalFunction")
"PrintDetails" = union("Estimate", "Confint",
                   "PosSemDefSymmMatrix",
                   "ParamFamParameter", "ParamFamily")
##########################
Symmetry classes            (other classes moved to package "distr")
##########################
slots:
type(character), SymmCenter(ANY)
"Symmetry"   (from package "distr")
|>"FunctionSymmetry"
|>|>"NonSymmetric"      [*]
|>|>"EvenSymmetric"     [*]
|>|>"OddSymmetric"      [*]
list thereof
"FunSymmList"           [*]
##########################
Matrix classes              (moved to package "distr")
##########################
slots:
none
"PosSemDefSymmMatrix" [*] is subclass of class "matrix" of package "base".
|>"PosDefSymmMatrix"  [*]
##########################
Norm Classes
##########################
slots:
name(character), fct(function)
"NormType"        [*]
|>"QFNorm"        [*]
Additional slots:
QuadForm(PosSemDefSymmMatrix)
|>|>"InfoNorm"    [*]
|>|>"SelfNorm"    [*]
##########################
Bias Classes
##########################
slots:
name(character)
"BiasType"
|>"symmetricBias"   [*]
|>"onesidedBias"
Additional slots:
sign(numeric)
|>"asymmetricBias"  [*]
Additional slots:
nu(numeric)
##########################
Risk Classes
##########################
slots:
type(character)
"RiskType"
|>"asRisk"
|>|>"asCov"       [*]
|>|>"trAsCov"     [*]
|>"fiRisk"
|>|>"fiCov"       [*]
|>|>"trfiCov"     [*]
|>|>"fiHampel"    [*]
Additional slots:
bound(numeric)
|>|>"fiMSE"       [*]
|>|>"fiBias"      [*]
|>|>"fiUnOvShoot" [*]
Additional slots:
width(numeric)
Risk with Bias:
"asRiskwithBias"
slots: biastype(BiasType), normtype(NormType),
|>"asHampel"      [*]
Additional slots:
bound(numeric)
|>"asBias"        [*]
|>"asGRisk"
|>|>"asMSE"       [*]
|>|>"asUnOvShoot" [*]
Additional slots:
width(numeric)
|>|>"asSemivar"   [*]
##########################
Estimate Classes
##########################
slots:
name(character), estimate(ANY),
samplesize(numeric), asvar(OptionalMatrix),
Infos(matrix), nuis.idx(OptionalNumeric)
fixed.estimate(OptionalNumeric),
estimate.call(call), trafo(list[of function, matrix]),
untransformed.estimate(ANY),
untransformed.asvar(OptionalMatrix)
criterion.fct(function), method(character),
"Estimate"
|>"MCEstimate",
Additional slots:
criterion(numeric)
##########################
Confidence interval class
##########################
slots:
type(character), confint(array),
estimate.call(call), name.estimate(character),
trafo.estimate(list[of function, matrix]),
nuisance.estimate(OptionalNumeric)
"Confint"

Methods

besides accessor and replacement functions, we have methods solve, sqrt for matrices checkL2deriv, existsPIC for class L2ParamFamily LogDeriv for class L2GroupParamFamily validParameter for classes ParamFamily, L2ScaleFamily, L2LocationFamily, and L2LocationScaleFamily modifyModel for the pairs of classes L2ParamFamily and ParamFamParameter, L2LocationFamily and ParamFamParameter, L2ScaleFamily and ParamFamParameter, L2LocationScaleFamily and ParamFamParameter, GammaFamily and ParamFamParameter, and ExpScaleFamily and ParamFamParameter mceCalc for the pair of classes numeric and ParamFamily mleCalc for the pairs of classes numeric and ParamFamily, numeric and BinomFamily, numeric and PoisFamily, numeric and NormLocationFamily, numeric and NormScaleFamily, and numeric and NormLocationScaleFamily coerce from class MCEstimate to class mle confint for class Estimate profile for class MCEstimate

Functions

Management of global options:
"distrModOptions", "distrModoptions", "getdistrModOption",
check for ker of matrix: "isKerAinKerB"
particular norms: "EuclideanNorm", "QuadFormNorm"
onesided bias: "positiveBias", "negativeBias",
Estimators:
"Estimator", "MCEstimator", "MLEstimator", "MDEstimator"
special location/scale models:
"L2LocationUnknownScaleFamily", "L2ScaleUnknownLocationFamily"
some special normal models:
"NormScaleUnknownLocationFamily", "NormLocationUnknownScaleFamily",

Start-up-Banner

You may suppress the start-up banner/message completely by setting options("StartupBanner"="off") somewhere before loading this package by library or require in your R-code / R-session. If option "StartupBanner" is not defined (default) or setting options("StartupBanner"=NULL) or options("StartupBanner"="complete") the complete start-up banner is displayed. For any other value of option "StartupBanner" (i.e., not in c(NULL,"off","complete")) only the version information is displayed. The same can be achieved by wrapping the library or require call into either suppressStartupMessages() or onlytypeStartupMessages(.,atypes="version"). As for general packageStartupMessage's, you may also suppress all the start-up banner by wrapping the library or require call into suppressPackageStartupMessages() from startupmsg-version 0.5 on.

Demos

Demos are available — see demo(package="distrMod").

Scripts

Example scripts are available — see folder ‘scripts’ in the package folder to package distrMod in your library.

Package versions

Note: The first two numbers of package versions do not necessarily reflect package-individual development, but rather are chosen for the distrXXX family as a whole in order to ease updating "depends" information.

Note

Some functions of packages stats, base have intentionally been masked, but completely retain their functionality — see distrModMASK(). If any of the packages stats4, fBasics is to be used together with distrMod, the latter must be attached after any of the first mentioned. Otherwise confint() defined as method in distrMod may get masked.
To re-mask, you may use confint <- distrMod::confint. See also distrModMASK()

Author(s)

Peter Ruckdeschel [email protected],
Matthias Kohl [email protected]
Maintainer: Peter Ruckdeschel [email protected]

References

M. Kohl and P. Ruckdeschel (2010): R Package distrMod: S4 Classes and Methods for Probability Models. Journal of Statistical Software, 35(10), 1-27. doi:10.18637/jss.v035.i10 (see also vignette("distrMod")) P. Ruckdeschel, M. Kohl, T. Stabla, F. Camphausen (2006): S4 Classes for Distributions, R News, 6(2), 2-6. https://CRAN.R-project.org/doc/Rnews/Rnews_2006-2.pdf A vignette for packages distr, distrSim, distrTEst, and distrEx is included into the mere documentation package distrDoc and may be called by require("distrDoc");vignette("distr")


Methods for Function .checkEstClassForParamFamily in Package ‘distrMod’

Description

.checkEstClassForParamFamily-methods

Usage

.checkEstClassForParamFamily(PFam, estimator)
## S4 method for signature 'ANY,ANY'
.checkEstClassForParamFamily(PFam, estimator)

Arguments

PFam

a parametric family.

estimator

an estimator.

Details

The respective methods can be used to cast an estimator to a model-specific subclass with particular methods.

Value

The (default) ANY,ANY-method returns the estimator unchanged.

Author(s)

Peter Ruckdeschel [email protected]


"addAlphTrsp2col"

Description

Adds alpha transparency to a given color.

Usage

addAlphTrsp2col(col, alpha=255)

Arguments

col

any valid color

alpha

tranparancy; an integer value in [0,255]

Value

a color in rgb coordinates

Author(s)

Peter Ruckdeschel [email protected]

Examples

## IGNORE_RDIFF_BEGIN
  addAlphTrsp2col(rgb(1,0.3,0.03), 25)
  ## gives "#FF4C0819" on 32bit and "#FF4D0819" on 64bit
## IGNORE_RDIFF_END
  addAlphTrsp2col("darkblue", 25)
  addAlphTrsp2col("#AAAAAAAA",25)
  palette(rainbow(6))
  addAlphTrsp2col(2, 25)

Generating function for asBias-class

Description

Generates an object of class "asBias".

Usage

asBias(biastype = symmetricBias(), normtype = NormType())

Arguments

biastype

a bias type of class BiasType

normtype

a norm type of class NormType

Value

Object of class "asBias"

Author(s)

Matthias Kohl [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

asBias-class

Examples

asBias()

## The function is currently defined as
function(biastype = symmetricBias(), normtype = NormType()){ 
     new("asBias",biastype = biastype, normtype = normtype) }

Standardized Asymptotic Bias

Description

Class of standardized asymptotic bias; i.e., the neighborhood radius is omitted respectively, set to 11.

Objects from the Class

Objects can be created by calls of the form new("asBias", ...). More frequently they are created via the generating function asBias.

Slots

type

Object of class "character": “asymptotic bias”.

biastype

Object of class "BiasType": symmetric, one-sided or asymmetric

normtype

Object of class "NormType": norm in which a multivariate parameter is considered

Extends

Class "asRiskwithBias", directly.
Class "asRisk", by class "asRiskwithBias"
Class "RiskType", by class "asRisk".

Author(s)

Matthias Kohl [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

asRisk-class, asBias

Examples

new("asBias")

Generating function for asCov-class

Description

Generates an object of class "asCov".

Usage

asCov()

Value

Object of class "asCov"

Author(s)

Matthias Kohl [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

asCov-class

Examples

asCov()

## The function is currently defined as
function(){ new("asCov") }

Asymptotic covariance

Description

Class of asymptotic covariance.

Objects from the Class

Objects can be created by calls of the form new("asCov", ...). More frequently they are created via the generating function asCov.

Slots

type

Object of class "character": “asymptotic covariance”.

Extends

Class "asRisk", directly.
Class "RiskType", by class "asRisk".

Methods

No methods defined with class "asCov" in the signature.

Author(s)

Matthias Kohl [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

asRisk-class, asCov

Examples

new("asCov")

Convex asymptotic risk

Description

Class of special convex asymptotic risks.

Objects from the Class

A virtual Class: No objects may be created from it.

Slots

type

Object of class "character".

biastype

Object of class "BiasType": symmetric, one-sided or asymmetric

normtype

Object of class "NormType": norm in which a multivariate parameter is considered

Extends

Class "asRisk", directly.
Class "RiskType", by class "asRisk".

Methods

No methods defined with class "asGRisk" in the signature.

Author(s)

Matthias Kohl [email protected]

References

Ruckdeschel, P. and Rieder, H. (2004) Optimal Influence Curves for General Loss Functions. Statistics & Decisions 22, 201-223.

See Also

asRisk-class


Generating function for asHampel-class

Description

Generates an object of class "asHampel".

Usage

asHampel(bound = Inf, biastype = symmetricBias(), normtype = NormType())

Arguments

bound

positive real: bias bound

biastype

a bias type of class BiasType

normtype

a norm type of class NormType

Value

Object of class asHampel

Author(s)

Matthias Kohl [email protected]

References

Hampel et al. (1986) Robust Statistics. The Approach Based on Influence Functions. New York: Wiley.

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

asHampel-class

Examples

asHampel()

## The function is currently defined as
function(bound = Inf, biastype = symmetricBias(), normtype = NormType()){ 
    new("asHampel", bound = bound, biastype = biastype, normtype = normtype) }

Asymptotic Hampel risk

Description

Class of asymptotic Hampel risk which is the trace of the asymptotic covariance subject to a given bias bound (bound on gross error sensitivity).

Objects from the Class

Objects can be created by calls of the form new("asHampel", ...). More frequently they are created via the generating function asHampel.

Slots

type

Object of class "character": “trace of asymptotic covariance for given bias bound”.

bound

Object of class "numeric": given positive bias bound.

biastype

Object of class "BiasType": symmetric, one-sided or asymmetric

Extends

Class "asRiskwithBias", directly.
Class "asRisk", by class "asRiskwithBias". Class "RiskType", by class "asRisk".

Methods

bound

signature(object = "asHampel"): accessor function for slot bound.

show

signature(object = "asHampel")

Author(s)

Matthias Kohl [email protected]

References

Hampel et al. (1986) Robust Statistics. The Approach Based on Influence Functions. New York: Wiley.

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

asRisk-class, asHampel

Examples

new("asHampel")

Generating function for asMSE-class

Description

Generates an object of class "asMSE".

Usage

asMSE(biastype = symmetricBias(), normtype = NormType())

Arguments

biastype

a bias type of class BiasType

normtype

a norm type of class NormType

Value

Object of class "asMSE"

Author(s)

Matthias Kohl [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

asMSE-class

Examples

asMSE()

## The function is currently defined as
function(biastype = symmetricBias(), normtype = NormType()){ 
         new("asMSE", biastype = biastype, normtype = normtype) }

Asymptotic mean square error

Description

Class of asymptotic mean square error.

Objects from the Class

Objects can be created by calls of the form new("asMSE", ...). More frequently they are created via the generating function asMSE.

Slots

type

Object of class "character": “asymptotic mean square error”.

biastype

Object of class "BiasType": symmetric, one-sided or asymmetric

normtype

Object of class "NormType": norm in which a multivariate parameter is considered

Extends

Class "asGRisk", directly.
Class "asRiskwithBias", by class "asGRisk".
Class "asRisk", by class "asRiskwithBias".
Class "RiskType", by class "asGRisk".

Methods

No methods defined with class "asMSE" in the signature.

Author(s)

Matthias Kohl [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

asGRisk-class, asMSE

Examples

new("asMSE")

Aymptotic risk

Description

Class of asymptotic risks.

Objects from the Class

A virtual Class: No objects may be created from it.

Slots

type

Object of class "character".

Extends

Class "RiskType", directly.

Methods

No methods defined with class "asRisk" in the signature.

Author(s)

Matthias Kohl [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Ruckdeschel, P. and Rieder, H. (2004) Optimal Influence Curves for General Loss Functions. Statistics & Decisions (submitted).

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

RiskType-class


Aymptotic risk

Description

Class of asymptotic risks.

Objects from the Class

A “virtual” Class (although it does not contain "VIRTUAL"): No objects may be created from it.

Slots

type

Object of class "character".

biastype

Object of class "BiasType".

normtype

Object of class "NormType".

Extends

Class "RiskType", directly.

Methods

biastype

signature(object = "asRiskwithBias"): accessor function for slot biastype.

biastype<-

signature(object = "asRiskwithBias", value = "BiasType"): replacement function for slot biastype.

normtype

signature(object = "asRiskwithBias"): accessor function for slot normtype.

normtype<-

signature(object = "asRiskwithBias", value = "NormType"): replacement function for slot normtype.

norm

signature(object = "asRiskwithBias"): accessor function for slot fct of slot norm.

Author(s)

Matthias Kohl [email protected], Peter Ruckdeschel [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Ruckdeschel, P. and Rieder, H. (2004) Optimal Influence Curves for General Loss Functions. Statistics & Decisions 22, 201-223.

Ruckdeschel, P. (2005) Optimally One-Sided Bounded Influence Curves. Mathematical Methods in Statistics 14(1), 105-131.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

asRisk-class


Generating function for asSemivar-class

Description

Generates an object of class "asSemivar".

Usage

asSemivar(sign = 1)

Arguments

sign

positive (=1) or negative Bias (=-1)

Value

Object of class "asSemivar"

Author(s)

Peter Ruckdeschel [email protected]

References

Ruckdeschel, P. (2005) Optimally One-Sided Bounded Influence Curves. Mathematical Methods in Statistics 14(1), 105-131.

See Also

onesidedBias-class

Examples

asSemivar()

Semivariance Risk Type

Description

Class for semi-variance risk.

Objects from the Class

Objects can be created by calls of the form new("asSemivar", ...). More frequently they are created via the generating function asSemivar.

Slots

type

Object of class "character": “asymptotic mean square error”.

biastype

Object of class "BiasType": symmetric, one-sided or asymmetric

normtype

Object of class "NormType": norm in which a multivariate parameter is considered

Methods

sign

signature(object = "asSemivar"): accessor function for slot sign.

sign<-

signature(object = "asSemivar", value = "numeric"): replacement function for slot sign.

Extends

Class "asGRisk", directly.
Class "asRiskwithBias", by class "asGRisk".
Class "asRisk", by class "asRiskwithBias".
Class "RiskType", by class "asGRisk".

Author(s)

Peter Ruckdeschel [email protected]

References

Ruckdeschel, P. (2005) Optimally One-Sided Bounded Influence Curves. Mathematical Methods in Statistics 14(1), 105-131.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

asGRisk-class, asMSE

Examples

asSemivar()

Generating function for asUnOvShoot-class

Description

Generates an object of class "asUnOvShoot".

Usage

asUnOvShoot(width = 1.960, biastype = symmetricBias())

Arguments

width

positive real: half the width of given confidence interval.

biastype

a bias type of class BiasType

Value

Object of class "asUnOvShoot"

Author(s)

Matthias Kohl [email protected]

References

Rieder, H. (1980) Estimates derived from robust tests. Ann. Stats. 8: 106–115.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

asUnOvShoot-class

Examples

asUnOvShoot()

## The function is currently defined as
function(width = 1.960, biastype = symmetricBias()){ 
     new("asUnOvShoot", width = width, biastype = biastype) }

Asymptotic under-/overshoot probability

Description

Class of asymptotic under-/overshoot probability.

Objects from the Class

Objects can be created by calls of the form new("asUnOvShoot", ...). More frequently they are created via the generating function asUnOvShoot.

Slots

type

Object of class "character": “asymptotic under-/overshoot probability”.

width

Object of class "numeric": half the width of given confidence interval.

biastype

Object of class "BiasType": symmetric, one-sided or asymmetric

Extends

Class "asGRisk", directly.
Class "asRiskwithBias", by class "asGRisk".
Class "asRisk", by class "asRiskwithBias".
Class "RiskType", by class "asGRisk".

Methods

width

signature(object = "asUnOvShoot"): accessor function for slot width.

show

signature(object = "asUnOvShoot")

Author(s)

Matthias Kohl [email protected]

References

Rieder, H. (1980) Estimates derived from robust tests. Ann. Stats. 8: 106–115.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

asGRisk-class

Examples

new("asUnOvShoot")

Generating function for asymmetricBias-class

Description

Generates an object of class "asymmetricBias".

Usage

asymmetricBias(name = "asymmetric Bias", nu = c(1,1) )

Arguments

name

name of the bias type

nu

weights for negative and positive bias, respectively

Value

Object of class "asymmetricBias"

Author(s)

Peter Ruckdeschel [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Ruckdeschel, P. (2005) Optimally One-Sided Bounded Influence Curves. Mathematical Methods in Statistics 14(1), 105-131.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

asymmetricBias-class

Examples

asymmetricBias()

## The function is currently defined as
function(){ new("asymmetricBias", name = "asymmetric Bias", nu = c(1,1)) }

asymmetric Bias Type

Description

Class of asymmetric bias types.

Objects from the Class

Objects can be created by calls of the form new("asymmetricBias", ...). More frequently they are created via the generating function asymmetricBias.

Slots

name

Object of class "character".

nu

Object of class "numeric"; to be in (0,1] x (0,1] with maximum 1; weights for negative and positive bias, respectively

Methods

nu

signature(object = "asymmetricBias"): accessor function for slot nu.

nu<-

signature(object = "asymmetricBias", value = "numeric"): replacement function for slot nu.

Extends

Class "BiasType", directly.

Author(s)

Peter Ruckdeschel [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Ruckdeschel, P. (2005) Optimally One-Sided Bounded Influence Curves. Mathematical Methods in Statistics 14(1), 105-131.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

BiasType-class

Examples

asymmetricBias()
## The function is currently defined as
function(){ new("asymmetricBias", name = "asymmetric Bias", nu = c(1,1)) }

aB <- asymmetricBias()
nu(aB)
try(nu(aB) <- -2) ## error
nu(aB) <- c(0.3,1)

Generating function for Beta families

Description

Generates an object of class "L2ParamFamily" which represents a Beta family.

Usage

BetaFamily(shape1 = 1, shape2 = 1, trafo, withL2derivDistr = TRUE)

Arguments

shape1

positive real: shape1 parameter

shape2

positive real: shape2 parameter

trafo

matrix: transformation of the parameter

withL2derivDistr

logical: shall the distribution of the L2 derivative be computed? Defaults to TRUE; setting it to FALSE speeds up computations.

Details

The slots of the corresponding L2 differentiable parameteric family are filled.

Value

Object of class "L2ParamFamily"

Author(s)

Peter Ruckdeschel [email protected]

See Also

L2ParamFamily-class, Beta-class

Examples

(B1 <- BetaFamily())
FisherInfo(B1)
## IGNORE_RDIFF_BEGIN
checkL2deriv(B1)
## IGNORE_RDIFF_END

Bias Type

Description

Class of bias types.

Objects from the Class

A virtual Class: No objects may be created from it.

Slots

name

Object of class "character".

Methods

name

signature(object = "BiasType"): accessor function for slot name.

name<-

signature(object = "BiasType", value = "character"): replacement function for slot name.

Author(s)

Peter Ruckdeschel [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Ruckdeschel, P. (2005) Optimally One-Sided Bounded Influence Curves. Mathematical Methods in Statistics 14(1), 105-131.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

RiskType-class

Examples

aB <- positiveBias()
name(aB)

Generating function for Binomial families

Description

Generates an object of class "L2ParamFamily" which represents a Binomial family where the probability of success is the parameter of interest.

Usage

BinomFamily(size = 1, prob = 0.5, trafo)

Arguments

size

number of trials

prob

probability of success

trafo

function in param or matrix: transformation of the parameter

Details

The slots of the corresponding L2 differentiable parameteric family are filled.

Value

Object of class "L2ParamFamily"

Author(s)

Matthias Kohl [email protected]

References

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

L2ParamFamily-class, Binom-class

Examples

(B1 <- BinomFamily(size = 25, prob = 0.25))
plot(B1)
FisherInfo(B1)
checkL2deriv(B1)

Generating function for Cauchy location families

Description

Generates an object of class "L2LocationFamily" which represents a Cauchy location family.

Usage

CauchyLocationFamily(loc = 0, scale = 1, trafo)

Arguments

loc

location

scale

scale

trafo

function in param or matrix: transformation of the parameter

Details

The slots of the corresponding L2 differentiable parameteric family are filled.

Value

Object of class "L2LocationScaleFamily"

Author(s)

Peter Ruckdeschel [email protected]

References

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

L2ParamFamily-class, Cauchy-class

Examples

(C1 <- CauchyLocationFamily())
plot(C1)
FisherInfo(C1)
### need smaller integration range:
checkL2deriv(C1)

Generating function for Cauchy location and scale families

Description

Generates an object of class "L2LocationScaleFamily" which represents a Cauchy location and scale family.

Usage

CauchyLocationScaleFamily(loc = 0, scale = 1, trafo)

Arguments

loc

location

scale

scale

trafo

function in param or matrix: transformation of the parameter

Details

The slots of the corresponding L2 differentiable parameteric family are filled.

Value

Object of class "L2LocationScaleFamily"

Author(s)

Matthias Kohl [email protected]

References

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

L2ParamFamily-class, Cauchy-class

Examples

(C1 <- CauchyLocationScaleFamily())
## synonymous: C1 <- CauchyFamily()
plot(C1)
FisherInfo(C1)
### need smaller integration range:
distrExoptions("ElowerTruncQuantile"=1e-4,"EupperTruncQuantile"=1e-4)
checkL2deriv(C1)
distrExoptions("ElowerTruncQuantile"=1e-7,"EupperTruncQuantile"=1e-7)

Generic function for checking L2-derivatives

Description

Generic function for checking the L2-derivative of an L2-differentiable family of probability measures.

Usage

checkL2deriv(L2Fam, ...)
## S3 method for class 'relMatrix'
print(x,...)

Arguments

L2Fam

L2-differentiable family of probability measures

x

argument to be printed

...

additional parameters (ignored/for compatibility with S3 generic in case print.relMatrix)

Details

The precisions of the centering and the Fisher information are computed.

Value

A list with items maximum.deviation, cent, consist, and condition is invisibly returned, where maximum.deviation comprises the maximal absolute value of all entries in cent and consist, cent shows the expectation of L2deriv(L2Fam) (which should be 0), consist shows the difference between the Fisher information and cov(L2deriv(L2Fam)) (which should be 0), and condition is the condition number of the Fisher information.

Note

The return value gives the non-rounded values (which will be machine dependent), whereas on argument out==TRUE (the default) we only issue the values up to 5 digits which should be independent of the machine. For the output of relative differences, we adjust accuracy to the size of the maximal (absolute) value of the Fisher information. In case of the consistency condition, at positions where the denominator is 0, we print a "."; this is done through helper S3 method print.relMatrix.

Author(s)

Matthias Kohl [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

L2ParamFamily-class

Examples

F1 <- new("L2ParamFamily")
checkL2deriv(F1)

Confint-class

Description

Return value S4 classes for method “confint”.

Objects from the Class

Objects could in principle be created by calls of the form new("Confint", ...). The preferred form is to have them created via a call to confint.

Slots

type

Object of class "character": type of the confidence interval (asymptotic, bootstrap,...). Can be of length >2. Then in printing, the first element is printed in the gap '[...]' in 'an [...] confidence interval', while the other elements are printed below.

confint

Object of class "array": the confidence interval(s).

call.estimate

Object of class "call": the estimate(s) for which the confidence intervals are produced.

name.estimate

Object of class "character": the name of the estimate(s) for which the confidence intervals are produced.

samplesize.estimate:

Object of class "numeric": the sample size of the estimate(s) for which the confidence intervals are (only complete cases) produced.

completecases.estimate:

Object of class "logical": complete cases at which the estimate was evaluated.

trafo.estimate

Object of class "matrix": the trafo/derivative matrix of the estimate(s) for which the confidence intervals are produced.

nuisance.estimate

Object of class "OptionalNumeric": the nuisance parameter (if any) at which the confidence intervals are produced.

fixed.estimate

Object of class "OptionalNumeric": the fixed part of the parameter (if any) at which the confidence intervals are produced.

Methods

type

signature(object = "Confint"): accessor function for slot type.

confint

signature(object = "Confint", method = "missing"): accessor function for slot type.

call.estimate

signature(object = "Confint"): accessor function for slot call.estimate.

name.estimate

signature(object = "Confint"): accessor function for slot name.estimate.

trafo.estimate

signature(object = "Confint"): accessor function for slot trafo.estimate.

samplesize.estimate

signature(object = "Confint"): (with additional argument onlycompletecases defaulting to TRUE returns the sample size; in case there are any incomplete cases and argument onlycompletecases is FALSE, the number of these is added to slot samplesize.

completecases.estimate

signature(object = "Confint"): accessor function for slot completecases.estimate.

nuisance.estimate

signature(object = "Confint"): accessor function for slot nuisance.estimate.

fixed.estimate

signature(object = "Confint"): accessor function for slot fixed.estimate.

show

signature(object = "Confint"): shows a detailed view of the object; slots nuisance.estimate and fixed.estimate are only shown if non-null, and slot trafo.estimate only if different from a unit matrix.

print

signature(object = "Confint"): just as show, but with additional arguments digits.

Details for methods 'show', 'print'

Detailedness of output by methods show, print is controlled by the global option show.details to be set by distrModoptions.

As method show is used when inspecting an object by typing the object's name into the console, show comes without extra arguments and hence detailedness must be controlled by global options.

Method print may be called with a (partially matched) argument show.details, and then the global option is temporarily set to this value.

More specifically, when show.detail is matched to "minimal" you will be shown only the type of the confidence interval(s) and its/their values. When show.detail is matched to "medium", you will in addition see the type of the estimator(s) for which it is produced, the corresponding call of the estimater, its sample size, and, if present, the value of the corresponding nuisance parameter. Finally, when show.detail is matched to "maximal", additionally you will be shown the fixed part of the parameter (if present) and the transformation of the estimator (if non-trivial, i.e. the identity) in form of its function code respectively of its derivative matrix.

Note

The pretty-printing code for methods show and print has been borrowed from confint.default in package stats.

Author(s)

Peter Ruckdeschel [email protected]

See Also

Estimator, confint, Estimate-class, trafo-methods

Examples

## some transformation
mtrafo <- function(x){
     nms0 <- c("scale","shape")
     nms <- c("shape","rate")
     fval0 <- c(x[2], 1/x[1])
     names(fval0) <- nms
     mat0 <- matrix( c(0, -1/x[1]^2, 1, 0), nrow = 2, ncol = 2,
                     dimnames = list(nms,nms0))                          
     list(fval = fval0, mat = mat0)}

x <- rgamma(50, scale = 0.5, shape = 3)

## parametric family of probability measures
G <- GammaFamily(scale = 1, shape = 2, trafo = mtrafo)
## MLE
res <- MLEstimator(x = x, ParamFamily = G)
ci <- confint(res)
print(ci, digits = 4, show.details="maximal")
print(ci, digits = 4, show.details="medium")
print(ci, digits = 4, show.details="minimal")

Methods for function confint in Package ‘distrMod’

Description

Methods for function confint in package distrMod; by default uses confint and its corresponding S3-methods, but also computes (asymptotic) confidence intervals for objects of class Estimate. Computes confidence intervals for one or more parameters in a fitted model.

Usage

confint(object, method, ...)
## S4 method for signature 'ANY,missing'
confint(object, method, parm, level = 0.95, ...)
## S4 method for signature 'Estimate,missing'
confint(object, method, level = 0.95)
## S4 method for signature 'mle,missing'
confint(object, method, parm, level = 0.95, ...)
## S4 method for signature 'profile.mle,missing'
confint(object, method, parm, level = 0.95, ...)

Arguments

object

in default / signature ANY case: a fitted model object, in signature Estimate case, an object of class Estimate

parm

only used in default / signature ANY case: a specification of which parameters are to be given confidence intervals, either a vector of numbers or a vector of names. If missing, all parameters are considered.

level

the confidence level required.

method

not yet used (only as missing; later to allow for various methods

...

additional argument(s) for methods.

Details

confint is a generic function. Its behavior differs according to its arguments.

signature ANY,missing:

the default method; uses the S3 generic of package stats, see confint; its return value is a matrix (or vector) with columns giving lower and upper confidence limits for each parameter. These will be labelled as (1-level)/2 and 1 - (1-level)/2 in % (by default 2.5% and 97.5%).

signature Estimate,missing:

will return an object of class Confint which corresponds to a confidence interval assuming asymptotic normality, and hence needs suitably filled slot asvar in argument object. Besides the actual bounds, organized in an array just as in the S3 generic, the return value also captures the name of the estimator for which it is produced, as well as the corresponding call producing the estimator, and the corresponding trafo and nuisance slots/parts.

See Also

confint, confint.glm and confint.nls in package MASS, Confint-class.

Examples

## for signature ANY examples confer stats::confint
## (empirical) Data
x <- rgamma(50, scale = 0.5, shape = 3)

## parametric family of probability measures
G <- GammaFamily(scale = 1, shape = 2)

## Maximum likelihood estimator
res <- MLEstimator(x = x, ParamFamily = G)
confint(res)

### for comparison:
require(MASS)
(res1 <- fitdistr(x, "gamma"))
## add a convenient (albeit wrong)
## S3-method for vcov:
## --- wrong as in general cov-matrix
##     will not be diagonal
## but for conf-interval this does
## not matter...
vcov.fitdistr <- function(object, ...){
     v<-diag(object$sd^2)
     rownames(v) <- colnames(v) <- names(object$estimate) 
     v}

## explicitely transforming to
## MASS parametrization:
mtrafo <- function(x){
     nms0 <- names(c(main(param(G)),nuisance(param(G))))
     nms <- c("shape","rate")
     fval0 <- c(x[2], 1/x[1])
     names(fval0) <- nms
     mat0 <- matrix( c(0, -1/x[1]^2, 1, 0), nrow = 2, ncol = 2,
                     dimnames = list(nms,nms0))                          
     list(fval = fval0, mat = mat0)}

G2 <- G
trafo(G2) <- mtrafo
res2 <- MLEstimator(x = x, ParamFamily = G2)

old<-getdistrModOption("show.details")
distrModoptions("show.details" = "minimal")
res
res1
res2
confint(res)
confint(res1)
confint(res2)
confint(res,level=0.99)
distrModoptions("show.details" = old)

Masking of/by other functions in package "distrMod"

Description

Provides information on the (intended) masking of and (non-intended) masking by other other functions in package distrMod

Usage

distrModMASK(library = NULL)

Arguments

library

a character vector with path names of R libraries, or NULL. The default value of NULL corresponds to all libraries currently known. If the default is used, the loaded packages are searched before the libraries

Value

no value is returned

Author(s)

Peter Ruckdeschel [email protected]

Examples

## IGNORE_RDIFF_BEGIN
distrModMASK()
## IGNORE_RDIFF_END

Function to change the global variables of the package ‘distrMod’

Description

With distrModOptions you can inspect and change the global variables of the package distrMod.

Usage

distrModOptions(...)
getdistrModOption(x)
distrModoptions(...)

Arguments

...

any options can be defined, using name = value or by passing a list of such tagged values.

x

a character string holding an option name.

Details

Invoking distrModoptions() with no arguments returns a list with the current values of the options. To access the value of a single option, one should use getdistrModOption("show.details"), e.g., rather than distrModoptions("show.details") which is a list of length one.

Value

distrModoptions() returns a list of the global options of distrMod.
distrModoptions("show.details") returns the global option show.details as a list of length 1.
distrModoptions("show.details" = "minimal") sets the value of the global option show.details to "minimal". getdistrModOption("show.details") the current value set for option show.details.

distrModoptions

For compatibility with spelling in package distr, distrModoptions is just a synonym to distrModoptions.

Currently available options

show.details

degree of detailedness for method show for objects of classes of the distrXXX family of packages. Possible values are

"maximal"

all information is shown

"minimal"

only the most important information is shown

"medium"

somewhere in the middle; see actual show-methods for details.

The default value is "maximal".

Author(s)

Matthias Kohl [email protected],
Peter Ruckdeschel [email protected]

See Also

options, getOption, distroptions, getdistrOption

Examples

distrModoptions()
distrModoptions("show.details")
distrModoptions("show.details" = "maximal")
distrModOptions("show.details" = "minimal")
# or
getdistrModOption("show.details")

Estimate-class.

Description

Class of estimates.

Objects from the Class

Objects can be created by calls of the form new("Estimate", ...). More frequently they are created via the generating function Estimator.

Slots

name

Object of class "character": name of the estimator.

estimate

Object of class "ANY": estimate.

estimate.call

Object of class "call": call by which estimate was produced.

Infos

object of class "matrix" with two columns named method and message: additional informations.

asvar

object of class "OptionalNumericOrMatrix" which may contain the asymptotic (co)variance of the estimator.

samplesize

object of class "numeric" — the samplesize (only complete cases are counted) at which the estimate was evaluated.

completecases

object of class "logical" — complete cases at which the estimate was evaluated.

nuis.idx

object of class "OptionalNumeric": indices of estimate belonging to the nuisance part.

fixed

object of class "OptionalNumeric": the fixed and known part of the parameter.

trafo

object of class "list": a list with components fct and mat (see below).

untransformed.estimate

Object of class "ANY": untransformed estimate.

untransformed.asvar

object of class "OptionalNumericOrMatrix" which may contain the asymptotic (co)variance of the untransformed estimator.

Methods

name

signature(object = "Estimate"): accessor function for slot name.

name<-

signature(object = "Estimate"): replacement function for slot name.

estimate

signature(object = "Estimate"): accessor function for slot estimate.

untransformed.estimate

signature(object = "Estimate"): accessor function for slot untransformed.estimate.

estimate.call

signature(object = "Estimate"): accessor function for slot estimate.call.

samplesize

signature(object = "Estimate"): (with additional argument onlycompletecases defaulting to TRUE returns the sample size; in case there are any incomplete cases and argument onlycompletecases is FALSE, the number of these is added to slot samplesize.

completecases

signature(object = "Estimate"): accessor function for slot completecases.

asvar

signature(object = "Estimate"): accessor function for slot asvar.

asvar<-

signature(object = "Estimate"): replacement function for slot asvar.

untransformed.asvar

signature(object = "Estimate"): accessor function for slot untransformed.asvar.

nuisance

signature(object = "Estimate"): accessor function for nuisance part of slot estimate.

main

signature(object = "Estimate"): accessor function for main part of slot estimate.

fixed

signature(object = "Estimate"): accessor function for slot fixed.

Infos

signature(object = "Estimate"): accessor function for slot Infos.

Infos<-

signature(object = "Estimate"): replacement function for slot Infos.

addInfo<-

signature(object = "Estimate"): function to add an information to slot Infos.

show

signature(object = "Estimate")

print

signature(object = "Estimate"): just as show, but with additional arguments digits.

Details for methods 'show', 'print'

Detailedness of output by methods show, print is controlled by the global option show.details to be set by distrModoptions.

As method show is used when inspecting an object by typing the object's name into the console, show comes without extra arguments and hence detailedness must be controlled by global options.

Method print may be called with a (partially matched) argument show.details, and then the global option is temporarily set to this value.

More specifically, when show.detail is matched to "minimal" you will be shown only the name/type of the estimator, the value of its main part, and, if present, the corresponding standard errors, as well as, also if present, the value of the nuisance part. When show.detail is matched to "medium", you will in addition see the class of the estimator, its call and its sample-size and, if present, the fixed part of the parameter and the asymptotic covariance matrix. Also the information gathered in the Infos slot is shown. Finally, when show.detail is matched to "maximal", and if, in addition, you estimate non-trivial (i.e. not the identity) transformation of the parameter of the parametric family, you will also be shown this transformation in form of its function and its derivative matrix at the estimated parameter value, as well as the estimator (with standard errors, if present) and (again, if present) the corresponding asymptotic covariance of the untransformed, total (i.e. main and nuisance part) parameter.

trafo realizes partial influence curves; i.e.; we are only interested is some possibly lower dimensional smooth (not necessarily linear or even coordinate-wise) aspect/transformation τ\tau of the parameter θ\theta.

To be coherent with the corresponding nuisance implementation, we make the following convention:

The full parameter θ\theta is split up coordinate-wise in a main parameter θ\theta' and a nuisance parameter θ\theta'' (which is unknown, too, hence has to be estimated, but only is of secondary interest) and a fixed, known part θ\theta'''.

Without loss of generality, we restrict ourselves to the case that transformation τ\tau only acts on the main parameter θ\theta' — if we want to transform the whole parameter, we only have to assume that both nuisance parameter θ\theta'' and fixed, known part of the parameter θ\theta''' have length 0.

To the implementation:

Slot trafo can either contain a (constant) matrix DθD_\theta or a function

τ ⁣:ΘΘ~,θτ(θ)\tau\colon \Theta' \to \tilde \Theta,\qquad \theta \mapsto \tau(\theta)

mapping main parameter θ\theta' to some range Θ~\tilde \Theta.

If slot value trafo is a function, besides τ(θ)\tau(\theta), it will also return the corresponding derivative matrix θτ(θ)\frac{\partial}{\partial \theta}\tau(\theta). More specifically, the return value of this function theta is a list with entries fval, the function value τ(θ)\tau(\theta), and mat, the derivative matrix.

In case trafo is a matrix DD, we interpret it as such a derivative matrix θτ(θ)\frac{\partial}{\partial \theta}\tau(\theta), and, correspondingly, τ(θ)\tau(\theta) as the linear mapping τ(θ)=Dθ\tau(\theta)=D\,\theta.

Note

The pretty-printing code for methods show and print has been borrowed from print.fitdistr in package MASS by B.D. Ripley.

Author(s)

Matthias Kohl [email protected],
Peter Ruckdeschel [email protected]

See Also

Estimator

Examples

x <- rnorm(100)
Estimator(x, estimator = mean, name = "mean")

x1 <- x; x1[sample(1:100,10)] <- NA
myEst1 <- Estimator(x1, estimator = mean, name = "mean")
samplesize(myEst1)
samplesize(myEst1, onlycomplete = FALSE)

Function to compute estimates

Description

The function Estimator provides a general way to compute estimates.

Usage

Estimator(x, estimator, name, Infos, asvar = NULL, nuis.idx,
          trafo = NULL, fixed = NULL, asvar.fct, na.rm = TRUE, ...,
          ParamFamily = NULL, .withEvalAsVar = TRUE)

Arguments

x

(empirical) data

estimator

function: estimator to be evaluated on x.

name

optional name for estimator.

Infos

character: optional informations about estimator

asvar

optionally the asymptotic (co)variance of the estimator

nuis.idx

optionally the indices of the estimate belonging to nuisance parameter

fixed

optionally (numeric) the fixed part of the parameter

trafo

an object of class MatrixorFunction – a transformation for the main parameter

asvar.fct

optionally: a function to determine the corresponding asymptotic variance; if given, asvar.fct takes arguments L2Fam(the parametric model as object of class L2ParamFamily) and param (the parameter value as object of class ParamFamParameter); arguments are called by name; asvar.fct may also process further arguments passed through the ... argument.

na.rm

logical: if TRUE, the estimator is evaluated at complete.cases(x).

...

further arguments to estimator.

ParamFamily

an optional object of class ParamFamily. Passed on to asvar.fct to compute asymptotic variances.

.withEvalAsVar

logical: shall slot asVar be evaluated (if asvar.fct is given) or just the call be returned?

Details

The argument criterion has to be a function with arguments the empirical data as well as an object of class "Distribution" and possibly ....

Value

An object of S4-class "Estimate".

Author(s)

Matthias Kohl [email protected],
Peter Ruckdeschel [email protected]

See Also

Estimate-class

Examples

x <- rnorm(100)
Estimator(x, estimator = mean, name = "mean")

X <- matrix(rnorm(1000), nrow = 10)
Estimator(X, estimator = rowMeans, name = "mean")

Generating function for EvenSymmetric-class

Description

Generates an object of class "EvenSymmetric".

Usage

EvenSymmetric(SymmCenter = 0)

Arguments

SymmCenter

numeric: center of symmetry

Value

Object of class "EvenSymmetric"

Author(s)

Matthias Kohl [email protected]

See Also

EvenSymmetric-class, FunctionSymmetry-class

Examples

EvenSymmetric()

## The function is currently defined as
function(SymmCenter = 0){ 
    new("EvenSymmetric", SymmCenter = SymmCenter) 
}

Class for Even Functions

Description

Class for even functions.

Objects from the Class

Objects can be created by calls of the form new("EvenSymmetric"). More frequently they are created via the generating function EvenSymmetric.

Slots

type

Object of class "character": contains “even function”

SymmCenter

Object of class "numeric": center of symmetry

Extends

Class "FunctionSymmetry", directly.
Class "Symmetry", by class "FunctionSymmetry".

Author(s)

Matthias Kohl [email protected]

See Also

EvenSymmetric, FunctionSymmetry-class

Examples

new("EvenSymmetric")

Methods for Function existsPIC in Package ‘distrMod’

Description

existsPIC-methods to check whether in a given L2 differentiable model at parameter value theta there exist (partial) influence curves to Trafo DθD_\theta.

Usage

existsPIC(object, ...)
## S4 method for signature 'L2ParamFamily'
existsPIC(object, warning = TRUE, tol = .Machine$double.eps^.5)

Arguments

object

L2ParamFamily

...

further arguments used by specific methods.

warning

logical: should a warning be issued if there exist no (partial) influence curves?

tol

the tolerance the linear algebraic operations. Default is .Machine$double.eps^.5.

Details

To check the existence of (partial) influence curves and, simultaneously, for bounded (partial) influence curves, by Lemma 1.1.3 in Kohl(2005) [resp. the fact that kerI=kerJ{\rm ker} I={\rm ker} J for J=E(Λ,1)(Λ,1)wJ= {\rm E} (\Lambda',1)' (\Lambda',1) w and w=min(1,b/(Λ,1)w={\rm min}(1, b/|(\Lambda',1)|], it suffices to check that kerI{\rm ker }I is a subset of kerDθ{\rm ker }D_\theta. This is done by a call to isKerAinKerB.

Author(s)

Peter Ruckdeschel [email protected]

References

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

isKerAinKerB


Generating function for exponential scale families

Description

Generates an object of class "L2ScaleFamily" which represents an exponential scale family.

Usage

ExpScaleFamily(scale = 1, trafo)

Arguments

scale

scale (= 1/rate)

trafo

function in param or matrix: optional transformation of the parameter

Details

The slots of the corresponding L2 differentiable parameteric family are filled. The scale parameter corresponds to 1/rate1/\code{rate}.

Value

Object of class "L2ScaleFamily"

Author(s)

Matthias Kohl [email protected]

References

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

L2ParamFamily-class, Exp-class

Examples

(E1 <- ExpScaleFamily())
plot(E1)
Map(L2deriv(E1)[[1]])
## IGNORE_RDIFF_BEGIN
checkL2deriv(E1)
## IGNORE_RDIFF_END

Generating function for fiBias-class

Description

Generates an object of class "fiBias".

Usage

fiBias()

Value

Object of class "fiBias"

Author(s)

Matthias Kohl [email protected]

References

Ruckdeschel, P. and Kohl, M. (2005) How to approximate the finite sample risk of M-estimators.

See Also

fiBias-class

Examples

fiBias()

## The function is currently defined as
function(){ new("fiBias") }

Finite-sample Bias

Description

Class of finite-sample bias.

Objects from the Class

Objects can be created by calls of the form new("fiBias", ...). More frequently they are created via the generating function fiBias.

Slots

type

Object of class "character": “finite-sample bias”.

Extends

Class "fiRisk", directly.
Class "RiskType", by class "fiRisk".

Methods

No methods defined with class "fiBias" in the signature.

Author(s)

Matthias Kohl [email protected]

References

Ruckdeschel, P. and Kohl, M. (2005) How to approximate the finite sample risk of M-estimators.

See Also

fiRisk-class, fiBias

Examples

new("fiBias")

Generating function for fiCov-class

Description

Generates an object of class "fiCov".

Usage

fiCov()

Value

Object of class "fiCov"

Author(s)

Matthias Kohl [email protected]

References

Ruckdeschel, P. and Kohl, M. (2005) How to approximate the finite sample risk of M-estimators.

See Also

fiCov-class

Examples

fiCov()

## The function is currently defined as
function(){ new("fiCov") }

Finite-sample covariance

Description

Class of finite-sample covariance.

Objects from the Class

Objects can be created by calls of the form new("fiCov", ...). More frequently they are created via the generating function fiCov.

Slots

type

Object of class "character": “finite-sample covariance”.

Extends

Class "fiRisk", directly.
Class "RiskType", by class "fiRisk".

Methods

No methods defined with class "fiCov" in the signature.

Author(s)

Matthias Kohl [email protected]

References

Ruckdeschel, P. and Kohl, M. (2005) How to approximate the finite sample risk of M-estimators.

See Also

fiRisk-class, fiCov

Examples

new("fiCov")

Generating function for fiHampel-class

Description

Generates an object of class "fiHampel".

Usage

fiHampel(bound = Inf)

Arguments

bound

positive real: bias bound

Value

Object of class fiHampel

Author(s)

Matthias Kohl [email protected]

References

Hampel et al. (1986) Robust Statistics. The Approach Based on Influence Functions. New York: Wiley.

Ruckdeschel, P. and Kohl, M. (2005) How to approximate the finite sample risk of M-estimators.

See Also

fiHampel-class

Examples

fiHampel()

## The function is currently defined as
function(bound = Inf){ new("fiHampel", bound = bound) }

Finite-sample Hampel risk

Description

Class of finite-sample Hampel risk which is the trace of the finite-sample covariance subject to a given bias bound (bound on gross error sensitivity).

Objects from the Class

Objects can be created by calls of the form new("fiHampel", ...). More frequently they are created via the generating function fiHampel.

Slots

type

Object of class "character": “trace of finite-sample covariance for given bias bound”.

bound

Object of class "numeric": given positive bias bound.

Extends

Class "fiRisk", directly.
Class "RiskType", by class "fiRisk".

Methods

bound

signature(object = "fiHampel"): accessor function for slot bound.

show

signature(object = "fiHampel")

Author(s)

Matthias Kohl [email protected]

References

Hampel et al. (1986) Robust Statistics. The Approach Based on Influence Functions. New York: Wiley.

Ruckdeschel, P. and Kohl, M. (2005) How to approximate the finite sample risk of M-estimators.

See Also

fiRisk-class, fiHampel

Examples

new("fiHampel")

Generating function for fiMSE-class

Description

Generates an object of class "fiMSE".

Usage

fiMSE()

Value

Object of class "fiMSE"

Author(s)

Matthias Kohl [email protected]

References

Ruckdeschel, P. and Kohl, M. (2005) How to approximate the finite sample risk of M-estimators.

See Also

fiMSE-class

Examples

fiMSE()

## The function is currently defined as
function(){ new("fiMSE") }

Finite-sample mean square error

Description

Class of asymptotic mean square error.

Objects from the Class

Objects can be created by calls of the form new("fiMSE", ...). More frequently they are created via the generating function fiMSE.

Slots

type

Object of class "character": “finite-sample mean square error”.

Extends

Class "fiRisk", directly.
Class "RiskType", by class "fiRisk".

Methods

No methods defined with class "fiMSE" in the signature.

Author(s)

Matthias Kohl [email protected]

References

Ruckdeschel, P. and Kohl, M. (2005) How to approximate the finite sample risk of M-estimators.

See Also

fiRisk-class, fiMSE

Examples

new("fiMSE")

Finite-sample risk

Description

Class of finite-sample risks.

Objects from the Class

A virtual Class: No objects may be created from it.

Slots

type

Object of class "character".

Extends

Class "RiskType", directly.

Methods

No methods defined with class "fiRisk" in the signature.

Author(s)

Matthias Kohl [email protected]

References

Ruckdeschel, P. and Kohl, M. (2005) How to approximate the finite sample risk of M-estimators.

See Also

RiskType-class


Generating function for fiUnOvShoot-class

Description

Generates an object of class "fiUnOvShoot".

Usage

fiUnOvShoot(width = 1.960)

Arguments

width

positive real: half the width of given confidence interval.

Value

Object of class "fiUnOvShoot"

Author(s)

Matthias Kohl [email protected]

References

Huber, P.J. (1968) Robust Confidence Limits. Z. Wahrscheinlichkeitstheor. Verw. Geb. 10:269–278.

Rieder, H. (1989) A finite-sample minimax regression estimator. Statistics 20(2): 211–221.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

Ruckdeschel, P. and Kohl, M. (2005) How to approximate the finite sample risk of M-estimators.

See Also

fiUnOvShoot-class

Examples

fiUnOvShoot()

## The function is currently defined as
function(width = 1.960){ new("fiUnOvShoot", width = width) }

Finite-sample under-/overshoot probability

Description

Class of finite-sample under-/overshoot probability.

Objects from the Class

Objects can be created by calls of the form new("fiUnOvShoot", ...). More frequently they are created via the generating function fiUnOvShoot.

Slots

type

Object of class "character": “finite-sample under-/overshoot probability”.

width

Object of class "numeric": half the width of given confidence interval.

Extends

Class "fiRisk", directly.
Class "RiskType", by class "fiRisk".

Methods

width

signature(object = "fiUnOvShoot"): accessor function for slot width.

show

signature(object = "fiUnOvShoot")

Author(s)

Matthias Kohl [email protected]

References

Huber, P.J. (1968) Robust Confidence Limits. Z. Wahrscheinlichkeitstheor. Verw. Geb. 10:269–278.

Rieder, H. (1989) A finite-sample minimax regression estimator. Statistics 20(2): 211–221.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

Ruckdeschel, P. and Kohl, M. (2005) Computation of the Finite Sample Risk of M-estimators on Neighborhoods.

See Also

fiRisk-class

Examples

new("fiUnOvShoot")

Class of Symmetries for Functions

Description

Class of symmetries for functions.

Objects from the Class

A virtual Class: No objects may be created from it.

Slots

type

Object of class "character": discribes type of symmetry.

SymmCenter

Object of class "OptionalNumeric": center of symmetry.

Extends

Class "Symmetry", directly.

Author(s)

Matthias Kohl [email protected]

See Also

Symmetry-class, OptionalNumeric-class


Generating function for FunSymmList-class

Description

Generates an object of class "FunSymmList".

Usage

FunSymmList(...)

Arguments

...

Objects of class "FunctionSymmetry" which shall form the list of symmetry types.

Value

Object of class "FunSymmList"

Author(s)

Matthias Kohl [email protected]

See Also

FunSymmList-class

Examples

FunSymmList(NonSymmetric(), EvenSymmetric(SymmCenter = 1), 
            OddSymmetric(SymmCenter = 2))

## The function is currently defined as
function (...){
    new("FunSymmList", list(...))
}

List of Symmetries for a List of Functions

Description

Create a list of symmetries for a list of functions

Objects from the Class

Objects can be created by calls of the form new("FunSymmList", ...). More frequently they are created via the generating function FunSymmList.

Slots

.Data

Object of class "list". A list of objects of class "FunctionSymmetry".

Extends

Class "list", from data part.
Class "vector", by class "list".

Author(s)

Matthias Kohl [email protected]

See Also

FunctionSymmetry-class

Examples

new("FunSymmList", list(NonSymmetric(), EvenSymmetric(SymmCenter = 1), 
                        OddSymmetric(SymmCenter = 2)))

Generating function for Gamma families

Description

Generates an object of class "L2ParamFamily" which represents a Gamma family.

Usage

GammaFamily(scale = 1, shape = 1, trafo, withL2derivDistr = TRUE)

Arguments

scale

positive real: scale parameter

shape

positive real: shape parameter

trafo

matrix: transformation of the parameter

withL2derivDistr

logical: shall the distribution of the L2 derivative be computed? Defaults to TRUE; setting it to FALSE speeds up computations.

Details

The slots of the corresponding L2 differentiable parameteric family are filled.

Value

Object of class "L2ParamFamily"

Author(s)

Matthias Kohl [email protected]

References

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

L2ParamFamily-class, Gammad-class

Examples

(G1 <- GammaFamily())
FisherInfo(G1)
## IGNORE_RDIFF_BEGIN
checkL2deriv(G1)
## IGNORE_RDIFF_END

Generating function for InfoNorm-class

Description

Generates an object of class "InfoNorm" — used for information-standardized influence curves.

Usage

InfoNorm()

Value

Object of class "InfoNorm"

Author(s)

Matthias Kohl [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

InfoNorm-class

Examples

## IGNORE_RDIFF_BEGIN
InfoNorm()

## The function is currently defined as
function(){ new("InfoNorm") }
## IGNORE_RDIFF_END

isKerAinKerB

Description

For two matrices A and B checks whether the null space of A is a subspace of the null space of B, in other words, if Ax=0Ax=0 entails Bx=0.

Usage

isKerAinKerB(A, B, tol = .Machine$double.eps)

Arguments

A

a matrix; if A is a vector, A is coerced to a matrix by as.matrix.

B

a matrix; if B is a vector, B is coerced to a matrix by as.matrix.

tol

the tolerance for detecting linear dependencies in the columns of a and up to which the two projectors are seen as equal (see below).

Details

via calls to svd, the projectors πA\pi_A and πB\pi_B onto the respective orthogonal complements of ker(A){\rm ker}(A) and ker(B){\rm ker}(B) are calculated and then is checked whether πBπA=πB\pi_B\pi_A=\pi_B.

Value

logical

Author(s)

Peter Ruckdeschel [email protected]

Examples

ma <- cbind(1,1,c(1,1,7))
D <- t(ma %*% c(0,1,-1))
## IGNORE_RDIFF_BEGIN
## note that results may vary according to BLAS
isKerAinKerB(D,ma)
isKerAinKerB(ma,D)
## IGNORE_RDIFF_END

L2 differentiable parametric group family

Description

Class of L2 differentiable parametric group families.

Objects from the Class

Objects can be created by calls of the form new("L2GroupParamFamily", ...). More frequently, this class is just used as an intermediate class to classes of specific group models like L2LocationFamily-class, L2ScaleFamily-class, and L2LocationScaleFamily-class.

Slots

name

[inherited from class "ProbFamily"] object of class "character": name of the family.

distribution

[inherited from class "ProbFamily"] object of class "Distribution": member of the family.

distrSymm

[inherited from class "ProbFamily"] object of class "DistributionSymmetry": symmetry of distribution.

param

[inherited from class "ParamFamily"] object of class "ParamFamParameter": parameter of the family.

fam.call

[inherited from class "ParamFamily"] object of class "call": call by which parametric family was produced.

makeOKPar

[inherited from class "ParamFamily"] object of class "function": has argument param — the (total) parameter, returns valid parameter; used if optim resp. optimize— try to use “illegal” parameter values; then makeOKPar makes a valid parameter value out of the illegal one.

startPar

[inherited from class "ParamFamily"] object of class "function": has argument x — the data, returns starting parameter for optim resp. optimize— a starting estimator in case parameter is multivariate or a search interval in case parameter is univariate.

modifyParam

[inherited from class "ParamFamily"] object of class "function": mapping from the parameter space (represented by "param") to the distribution space (represented by "distribution").

props

[inherited from class "ProbFamily"] object of class "character": properties of the family.

L2deriv

[inherited from class "L2ParamFamily"] object of class "EuclRandVariable": L2 derivative of the family.

L2deriv.fct

[inherited from class "L2ParamFamily"] object of class "function": mapping from the parameter space (argument param of class "ParamFamParameter") to a mapping from observation x to the value of the L2derivative; L2deriv.fct is then used from observation x to value of the L2derivative; L2deriv.fct is used by modifyModel to move the L2deriv according to a change in the parameter

L2derivSymm

[inherited from class "L2ParamFamily"] object of class "FunSymmList": symmetry of the maps included in L2deriv.

L2derivDistr

[inherited from class "L2ParamFamily"] object of class "UnivarDistrList": list which includes the distribution of L2deriv.

L2derivDistrSymm

[inherited from class "L2ParamFamily"] object of class "DistrSymmList": symmetry of the distributions included in L2derivDistr.

FisherInfo.fct

[inherited from class "L2ParamFamily"] object of class "function": mapping from the parameter space (argument param of class "ParamFamParameter") to the set of positive semidefinite matrices; FisherInfo.fct is used by modifyModel to move the Fisher information according to a change in the parameter

FisherInfo

[inherited from class "L2ParamFamily"] object of class "PosDefSymmMatrix": Fisher information of the family.

LogDeriv

object of class "function": has argument x; the negative logarithmic derivative of the density of the model distribution at the "standard" parameter value.

Extends

Class "L2ParamFamily", directly.
Class "ParamFamily", by class "L2ParamFamily".
Class "ProbFamily", by class "ParamFamily".

Methods

LogDeriv

signature(object = "L2GroupParamFamily"): accessor function for slot LogDeriv.

LogDeriv<-

signature(object = "L2GroupParamFamily"): replacement function for slot LogDeriv.

Author(s)

Peter Ruckdeschel [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

L2ParamFamily-class, ParamFamily-class

Examples

F1 <- new("L2GroupParamFamily")
plot(F1)

Generating function for L2LocationFamily-class

Description

Generates an object of class "L2LocationFamily".

Usage

L2LocationFamily(loc = 0, name, centraldistribution = Norm(),
                 locname = "loc", modParam, LogDeriv,  
                 L2derivDistr.0, FisherInfo.0, distrSymm, L2derivSymm, 
                 L2derivDistrSymm, trafo, .returnClsName = NULL)

Arguments

loc

numeric: location parameter of the model.

name

character: name of the parametric family.

centraldistribution

object of class "AbscontDistribution"; we assume from the beginning, that centraldistribution is symmetric about its median.

modParam

optional function: mapping from the parameter space (represented by "param") to the distribution space (represented by "distribution").

locname

a character vector of length 1 containing the name of the location parameter

LogDeriv

function with argument x: the negative logarithmic derivative of the density of the central distribution; if missing, it is determined numerically using numeric differentiation.

L2derivDistr.0

object of class "UnivariateDistribution": distribution of the L2derivative at the central distribution

FisherInfo.0

object of class "PosSemDefSymmMatrix": Fisher information of the model at the "standard" parameter value

distrSymm

object of class "DistributionSymmetry": symmetry of distribution.

L2derivSymm

object of class "FunSymmList": symmetry of the maps contained in L2deriv

L2derivDistrSymm

object of class "DistrSymmList": symmetry of the distributions contained in L2derivDistr

trafo

matrix or function in param: transformation of the parameter

.returnClsName

the class name of the return value; by default this argument is NULL whereupon the return class will be L2LocationScaleFamily; but, internally, this generating function is also used to produce objects of class Classes NormLocationFamily and GumbelLocationFamily (the latter in package RobExtremes.

Details

If name is missing, the default “L2 location family” is used. The function modParam is optional. If it is missing, it is constructed from centraldistribution using the location structure of the model. Slot param is filled accordingly with the argument trafo passed to L2LocationFamily. In case L2derivDistr.0 is missing, L2derivDistr is computed via imageDistr, else L2derivDistr is assigned L2derivDistr.0, coerced to "UnivariateDistributionList". In case FisherInfo.0 is missing, Fisher information is computed from L2deriv using E. If distrSymm is missing, it is set to symmetry about loc. If L2derivSymm is missing, it is set to no symmetry, and if L2derivDistrSymm is missing, it is set to no symmetry, too.

Value

Object of class "L2LocationFamily"

Author(s)

Matthias Kohl [email protected],
Peter Ruckdeschel [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

L2LocationFamily-class

Examples

F1 <- L2LocationFamily()
plot(F1)

L2 differentiable parametric group family

Description

Class of L2 differentiable parametric group families.

Objects from the Class

Objects can be created by calls of the form new("L2LocationFamily", ...). More frequently they are created via the generating function L2LocationFamily.

Slots

name

[inherited from class "ProbFamily"] object of class "character": name of the family.

distribution

[inherited from class "ProbFamily"] object of class "Distribution": member of the family.

distrSymm

[inherited from class "ProbFamily"] object of class "DistributionSymmetry": symmetry of distribution.

param

[inherited from class "ParamFamily"] object of class "ParamFamParameter": parameter of the family.

fam.call

[inherited from class "ParamFamily"] object of class "call": call by which parametric family was produced.

makeOKPar

[inherited from class "ParamFamily"] object of class "function": has argument param — the (total) parameter, returns valid parameter; used if optim resp. optimize— try to use “illegal” parameter values; then makeOKPar makes a valid parameter value out of the illegal one.

startPar

[inherited from class "ParamFamily"] object of class "function": has argument x — the data, returns starting parameter for optim resp. optimize— a starting estimator in case parameter is multivariate or a search interval in case parameter is univariate.

modifyParam

[inherited from class "ParamFamily"] object of class "function": mapping from the parameter space (represented by "param") to the distribution space (represented by "distribution").

props

[inherited from class "ProbFamily"] object of class "character": properties of the family.

L2deriv

[inherited from class "L2ParamFamily"] object of class "EuclRandVariable": L2 derivative of the family.

L2deriv.fct

[inherited from class "L2ParamFamily"] object of class "function": mapping from the parameter space (argument param of class "ParamFamParameter") to a mapping from observation x to the value of the L2derivative; L2deriv.fct is then used from observation x to value of the L2derivative; L2deriv.fct is used by modifyModel to move the L2deriv according to a change in the parameter

L2derivSymm

[inherited from class "L2ParamFamily"] object of class "FunSymmList": symmetry of the maps included in L2deriv.

L2derivDistr

[inherited from class "L2ParamFamily"] object of class "UnivarDistrList": list which includes the distribution of L2deriv.

L2derivDistrSymm

[inherited from class "L2ParamFamily"] object of class "DistrSymmList": symmetry of the distributions included in L2derivDistr.

FisherInfo.fct

[inherited from class "L2ParamFamily"] object of class "function": mapping from the parameter space (argument param of class "ParamFamParameter") to the set of positive semidefinite matrices; FisherInfo.fct is used by modifyModel to move the Fisher information according to a change in the parameter

FisherInfo

[inherited from class "L2ParamFamily"] object of class "PosDefSymmMatrix": Fisher information of the family.

LogDeriv

[inherited from class "L2GroupParamFamily"] object of class "function": has argument x; the negative logarithmic derivative of the density of the model distribution at the "standard" parameter value.

locscalename

[inherited from class "L2LocationScaleUnion"] object of class "character": names of location and scale parameter

Extends

Class "L2LocationScaleUnion", directly.
Class "L2GroupParamFamily", by class "L2LocationScaleUnion".
Class "L2ParamFamily", by class "L2GroupParamFamily".
Class "ParamFamily", by class "L2ParamFamily".
Class "ProbFamily", by class "ParamFamily".

Methods

modifyModel

signature(model = "L2LocationFamily", param = "ParamFamParameter"): moves the L2-location family model to parameter param

Author(s)

Matthias Kohl [email protected],
Peter Ruckdeschel [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

L2LocationFamily, ParamFamily-class

Examples

F1 <- new("L2LocationFamily")
plot(F1)

Generating function for L2LocationScaleFamily-class

Description

Generates an object of class "L2LocationScaleFamily".

Usage

L2LocationScaleFamily(loc = 0, scale = 1, name, centraldistribution = Norm(),
                      locscalename = c("loc", "scale"), modParam, LogDeriv,  
                      L2derivDistr.0, FisherInfo.0, distrSymm, L2derivSymm, 
                      L2derivDistrSymm, trafo, .returnClsName = NULL)

Arguments

loc

numeric: location parameter of the model.

scale

positive number: scale of the model.

name

character: name of the parametric family.

centraldistribution

object of class "AbscontDistribution": central distribution; we assume by default, that centraldistribution is symmetric about 00

modParam

optional function: mapping from the parameter space (represented by "param") to the distribution space (represented by "distribution").

locscalename

a character vector of length 2 containing the names of the location and scale parameter; either unnamed, then order must be c(loc,scale), or named, then names must be "loc" and "scale"

LogDeriv

function with argument x: the negative logarithmic derivative of the density of the central distribution; if missing, it is determined numerically using numeric differentiation.

L2derivDistr.0

list of length 2 of objects of class "UnivariateDistribution": (marginal) distributions of the coordinates of the L2derivative at the central distribution

FisherInfo.0

object of class "PosSemDefSymmMatrix": Fisher information of the model at the "standard" parameter value

distrSymm

object of class "DistributionSymmetry": symmetry of distribution.

L2derivSymm

object of class "FunSymmList": symmetry of the maps contained in L2deriv

L2derivDistrSymm

object of class "DistrSymmList": symmetry of the distributions contained in L2derivDistr

trafo

matrix or function in param: transformation of the parameter

.returnClsName

the class name of the return value; by default this argument is NULL whereupon the return class will be L2LocationScaleFamily; but, internally, this generating function is also used to produce objects of class NormalLocationScaleFamily, CauchyLocationScaleFamily.

Details

If name is missing, the default “L2 location and scale family” is used. The function modParam is optional. If it is missing, it is constructed from centraldistribution using the location and scale structure of the model. Slot param is filled accordingly with the argument trafo passed to L2LocationScaleFamily. In case L2derivDistr.0 is missing, L2derivDistr is computed via imageDistr, else L2derivDistr is assigned L2derivDistr.0, coerced to "UnivariateDistributionList". In case FisherInfo.0 is missing, Fisher information is computed from L2deriv using E. If distrSymm is missing, it is set to symmetry about loc. If L2derivSymm is missing, its location and scale components are set to no symmetry , respectively. if L2derivDistrSymm is missing, its location and scale components are set to no symmetry, respectively.

Value

Object of class "L2LocationScaleFamily"

Author(s)

Matthias Kohl [email protected],
Peter Ruckdeschel [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

L2LocationScaleFamily-class

Examples

F1 <- L2LocationScaleFamily()
plot(F1)

L2 differentiable parametric group family

Description

Class of L2 differentiable parametric group families.

Objects from the Class

Objects can be created by calls of the form new("L2LocationScaleFamily", ...). More frequently they are created via the generating function L2LocationScaleFamily.

Slots

name

[inherited from class "ProbFamily"] object of class "character": name of the family.

distribution

[inherited from class "ProbFamily"] object of class "Distribution": member of the family.

distrSymm

[inherited from class "ProbFamily"] object of class "DistributionSymmetry": symmetry of distribution.

param

[inherited from class "ParamFamily"] object of class "ParamFamParameter": parameter of the family.

fam.call

[inherited from class "ParamFamily"] object of class "call": call by which parametric family was produced.

makeOKPar

[inherited from class "ParamFamily"] object of class "function": has argument param — the (total) parameter, returns valid parameter; used if optim resp. optimize— try to use “illegal” parameter values; then makeOKPar makes a valid parameter value out of the illegal one.

startPar

[inherited from class "ParamFamily"] object of class "function": has argument x — the data, returns starting parameter for optim resp. optimize— a starting estimator in case parameter is multivariate or a search interval in case parameter is univariate.

modifyParam

[inherited from class "ParamFamily"] object of class "function": mapping from the parameter space (represented by "param") to the distribution space (represented by "distribution").

props

[inherited from class "ProbFamily"] object of class "character": properties of the family.

L2deriv

[inherited from class "L2ParamFamily"] object of class "EuclRandVariable": L2 derivative of the family.

L2deriv.fct

[inherited from class "L2ParamFamily"] object of class "function": mapping from the parameter space (argument param of class "ParamFamParameter") to a mapping from observation x to the value of the L2derivative; L2deriv.fct is then used from observation x to value of the L2derivative; L2deriv.fct is used by modifyModel to move the L2deriv according to a change in the parameter

L2derivSymm

[inherited from class "L2ParamFamily"] object of class "FunSymmList": symmetry of the maps included in L2deriv.

L2derivDistr

[inherited from class "L2ParamFamily"] object of class "UnivarDistrList": list which includes the distribution of L2deriv.

L2derivDistrSymm

[inherited from class "L2ParamFamily"] object of class "DistrSymmList": symmetry of the distributions included in L2derivDistr.

FisherInfo.fct

[inherited from class "L2ParamFamily"] object of class "function": mapping from the parameter space (argument param of class "ParamFamParameter") to the set of positive semidefinite matrices; FisherInfo.fct is used by modifyModel to move the Fisher information according to a change in the parameter

FisherInfo

[inherited from class "L2ParamFamily"] object of class "PosDefSymmMatrix": Fisher information of the family.

LogDeriv

[inherited from class "L2GroupParamFamily"] object of class "function": has argument x; the negative logarithmic derivative of the density of the model distribution at the "standard" parameter value.

locscalename

[inherited from class "L2LocationScaleUnion"] object of class "character": names of location and scale parameter

Extends

Class "L2LocationScaleUnion", directly.
Class "L2GroupParamFamily", by class "L2LocationScaleUnion".
Class "L2ParamFamily", by class "L2GroupParamFamily".
Class "ParamFamily", by class "L2ParamFamily".
Class "ProbFamily", by class "ParamFamily".

Methods

modifyModel

signature(model = "L2LocationScaleFamily", param = "ParamFamParameter"): moves the L2-location and scale family model to parameter param

Author(s)

Matthias Kohl [email protected],
Peter Ruckdeschel [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

L2LocationScaleFamily, ParamFamily-class

Examples

F1 <- new("L2LocationScaleFamily")
plot(F1)

Generating function for L2LocationScaleFamily-class in nuisance situation

Description

Generates an object of class "L2LocationScaleFamily" in the situation where location is main, scale nuisance parameter.

Usage

L2LocationUnknownScaleFamily(loc = 0, scale = 1, name, centraldistribution = Norm(),
                      locscalename = c("loc", "scale"), modParam, LogDeriv,  
                      L2derivDistr.0, FisherInfo.0, distrSymm, L2derivSymm, 
                      L2derivDistrSymm, trafo, .returnClsName = NULL)

Arguments

loc

numeric: location parameter of the model.

scale

positive number: scale of the model.

name

character: name of the parametric family.

centraldistribution

object of class "AbscontDistribution": central distribution; we assume by default, that centraldistribution is symmetric about 00

modParam

optional function: mapping from the parameter space (represented by "param") to the distribution space (represented by "distribution").

locscalename

a character vector of length 2 containing the names of the location and scale parameter; either unnamed, then order must be c(loc,scale), or named, then names must be "loc" and "scale"

LogDeriv

function with argument x: the negative logarithmic derivative of the density of the central distribution; if missing, it is determined numerically using numeric differentiation.

L2derivDistr.0

list of length 2 of objects of class "UnivariateDistribution": (marginal) distributions of the coordinates of the L2derivative at the central distribution

FisherInfo.0

object of class "PosSemDefSymmMatrix": Fisher information of the model at the "standard" parameter value

distrSymm

object of class "DistributionSymmetry": symmetry of distribution.

L2derivSymm

object of class "FunSymmList": symmetry of the maps contained in L2deriv

L2derivDistrSymm

object of class "DistrSymmList": symmetry of the distributions contained in L2derivDistr

trafo

matrix or function in param: transformation of the parameter

.returnClsName

the class name of the return value; by default this argument is NULL whereupon the return class will be L2LocationScaleFamily; but, internally, this generating function is also used to produce objects of class NormalLocationScaleFamily.

Details

If name is missing, the default “L2 location family with unknown scale (as nuisance)” is used. The function modParam is optional. If it is missing, it is constructed from centraldistribution using the location and scale structure of the model. Slot param is filled accordingly with the argument trafo passed to L2LocationUnknownScaleFamily. In case L2derivDistr.0 is missing, L2derivDistr is computed via imageDistr, else L2derivDistr is assigned L2derivDistr.0, coerced to "UnivariateDistributionList". In case FisherInfo.0 is missing, Fisher information is computed from L2deriv using E. If distrSymm is missing, it is set to symmetry about loc. If L2derivSymm is missing, its location and scale components are set to no symmetry, respectively. if L2derivDistrSymm is missing, its location and scale components are set to no symmetry, respectively.

Value

Object of class "L2LocationScaleFamily"

Author(s)

Peter Ruckdeschel [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

L2LocationScaleFamily-class

Examples

F1 <- L2LocationUnknownScaleFamily()
plot(F1)

Generating function for L2ParamFamily-class

Description

Generates an object of class "L2ParamFamily".

Usage

L2ParamFamily(name, distribution = Norm(), distrSymm, 
              main = main(param), nuisance = nuisance(param),
              fixed = fixed(param), trafo = trafo(param),
              param = ParamFamParameter(name = paste("Parameter of", name),  
                          main = main, nuisance = nuisance, 
                          fixed = fixed, trafo = trafo),
              props = character(0),
              startPar = NULL, makeOKPar = NULL,
              modifyParam = function(theta){ Norm(mean=theta) },
              L2deriv.fct = function(param) {force(theta <- param@main)
                           return(function(x) {x-theta})},
              L2derivSymm, L2derivDistr, L2derivDistrSymm, 
              FisherInfo.fct, FisherInfo = FisherInfo.fct(param),
              .returnClsName = NULL, .withMDE = TRUE)

Arguments

name

character string: name of the family

distribution

object of class "Distribution": member of the family

distrSymm

object of class "DistributionSymmetry": symmetry of distribution.

main

numeric vector: main parameter

nuisance

numeric vector: nuisance parameter

fixed

numeric vector: fixed part of the parameter

trafo

function in param or matrix: transformation of the parameter

param

object of class "ParamFamParameter": parameter of the family

startPar

startPar is a function in the observations x returning initial information for MCEstimator used by optimize resp. optim; i.e; if (total) parameter is of length 1, startPar returns a search interval, else it returns an initial parameter value.

makeOKPar

makeOKPar is a function in the (total) parameter param; used if optim resp. optimize— try to use “illegal” parameter values; then makeOKPar makes a valid parameter value out of the illegal one; if NULL slot makeOKPar of ParamFamily is used to produce it.

modifyParam

function: mapping from the parameter space (represented by "param") to the distribution space (represented by "distribution").

props

character vector: properties of the family

L2deriv.fct

function: mapping from the parameter space (argument param of class "ParamFamParameter") to a mapping from observation x to the value of the L2derivative; L2deriv.fct is used by modifyModel to move the L2deriv according to a change in the parameter, and to fill slot L2deriv. More specifically, let us call the parts main and nuisance of the parameter the unknown parameter. If this unknown parameter is one-dimensional, the return value of L2deriv.fct must be a function in argument x, which is vectorized, (i.e., callable for a vector-valued x), and has a one-dimensional, numeric return value. In case the dimension of the unknown parameter is larger than one, the return value must be a list of functions, each of which satisfies the conditions formulated for the case of a one-dimensional parameter of interest. The order of the components of this list is the same as the order of the parameter coordinates in main, followed by the ones in nuisance.

L2derivSymm

object of class "FunSymmList": symmetry of the maps contained in L2deriv; a list of symmetry properties of the same length as the return value of L2deriv.fct .

L2derivDistr

object of class "UnivarDistrList": distribution of L2deriv; the length of this list of univariate distributions must be of the same length as the return value of L2deriv.fct .

L2derivDistrSymm

object of class "DistrSymmList": symmetry of the distributions contained in L2derivDistr; the length of this list of symmetry properties must be of the same length as the return value of L2deriv.fct .

FisherInfo.fct

function: mapping from the parameter space (argument param of class "ParamFamParameter") to the set of positive semidefinite matrices; FisherInfo.fct is used by modifyModel to move the Fisher information according to a change in the parameter

FisherInfo

object of class "PosSemDefSymmMatrix": Fisher information of the family

.returnClsName

the class name of the return value; by default this argument is NULL whereupon the return class will be L2ParamFamily; but, internally, this generating function is also used to e.g. produce objects of class BinomialFamily, PoisFamily GammaFamily, BetaFamily.

.withMDE

logical of length 1: Tells R how to use the function from slot startPar in case of a kStepEstimator—use it as is or to compute the starting point for a minimum distance estimator which in turn then serves as starting point for roptest / robest (from package ROptEst). If TRUE (default) the latter alternative is used. Ignored if ROptEst is not used.

Details

If name is missing, the default “L2 differentiable parametric family of probability measures” is used. In case distrSymm is missing it is set to NoSymmetry(). If param is missing, the parameter is created via main, nuisance and trafo as described in ParamFamParameter. In case L2derivSymm is missing, it is filled with an object of class FunSymmList with entries NonSymmetric(). In case L2derivDistr is missing, it is computed via imageDistr. If L2derivDistrSymm is missing, it is set to an object of class DistrSymmList with entries NoSymmetry(). In case FisherInfo is missing, it is computed from L2deriv using E.

Value

Object of class "L2ParamFamily"

Author(s)

Matthias Kohl [email protected],
Peter Ruckdeschel [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

L2ParamFamily-class

Examples

F1 <- L2ParamFamily()
plot(F1)

L2 differentiable parametric family

Description

Class of L2 differentiable parametric families.

Details

In the E-methods, diagnostics on the involved integrations are available if argument diagnostic is TRUE. Then there is attribute diagnostic attached to the return value, which may be inspected and accessed through showDiagnostic and getDiagnostic.

Objects from the Class

Objects can be created by calls of the form new("L2ParamFamily", ...). More frequently they are created via the generating function L2ParamFamily.

Slots

name

[inherited from class "ProbFamily"] object of class "character": name of the family.

distribution

[inherited from class "ProbFamily"] object of class "Distribution": member of the family.

distrSymm

[inherited from class "ProbFamily"] object of class "DistributionSymmetry": symmetry of distribution.

param

[inherited from class "ParamFamily"] object of class "ParamFamParameter": parameter of the family.

fam.call

[inherited from class "ParamFamily"] object of class "call": call by which parametric family was produced.

makeOKPar

[inherited from class "ParamFamily"] object of class "function": has argument param — the (total) parameter, returns valid parameter; used if optim resp. optimize— try to use “illegal” parameter values; then makeOKPar makes a valid parameter value out of the illegal one.

startPar

[inherited from class "ParamFamily"] object of class "function": has argument x — the data, returns starting parameter for optim resp. optimize— a starting estimator in case parameter is multivariate or a search interval in case parameter is univariate.

modifyParam

[inherited from class "ParamFamily"] object of class "function": mapping from the parameter space (represented by "param") to the distribution space (represented by "distribution").

props

[inherited from class "ProbFamily"] object of class "character": properties of the family.

L2deriv

object of class "EuclRandVariable": L2 derivative of the family. Its map slot must contain a list of functions. Each function in this list must have just one argument x, which is vectorized, (i.e., callable for a vector-valued x), and has a one-dimensional, numeric return value.

L2deriv.fct

object of class "function": mapping from the parameter space (argument param of class "ParamFamParameter") to a mapping from observation x to the value of the L2derivative; L2deriv.fct is then used from observation x to value of the L2derivative; L2deriv.fct is used by modifyModel to move the L2deriv according to a change in the parameter. More specifically, let us call the parts main and nuisance of the parameter the unknown parameter. If this unknown parameter is one-dimensional, the return value of L2deriv.fct must be a function in argument x, which is vectorized, (i.e., callable for a vector-valued x), and has a one-dimensional, numeric return value. In case the dimension of the unknown parameter is larger than one, the return value must be a list of functions, each of which satisfies the conditions formulated for the case of a one-dimensional parameter of interest. The order of the components of this list is the same as the order of the parameter coordinates in main, followed by the ones in nuisance.

L2derivSymm

object of class "FunSymmList": symmetry of the maps contained in L2deriv; a list of symmetry properties of the same length as the return value of L2deriv.fct .

L2derivDistr

object of class "OptionalDistrListOrCall" (i.e., NULL or an object of class "DistrList" or the respective call to generate the latter object): if non-null and non-call, a list which includes the distribution of L2deriv; the length of this list of univariate distributions must be of the same length as the return value of L2deriv.fct .

L2derivDistrSymm

object of class "DistrSymmList": symmetry of the distributions contained in L2derivDistr; the length of this list of symmetry properties must be of the same length as the return value of L2deriv.fct .

FisherInfo.fct

object of class "function": mapping from the parameter space (argument param of class "ParamFamParameter") to the set of positive semidefinite matrices; FisherInfo.fct is used by modifyModel to move the Fisher information according to a change in the parameter

FisherInfo

object of class "PosDefSymmMatrix": Fisher information of the family.

.withEvalL2derivDistr

logical of length one: if TRUE slot L2derivDistr gets evaluated, otherwise it is only kept as call.

Extends

Class "ParamFamily", directly.
Class "ProbFamily", by class "ParamFamily".

Methods

L2deriv

signature(object = "L2ParamFamily"): accessor function for L2deriv.

L2deriv

signature(object = "L2ParamFamily", param = "ParamFamParameter"): returns the L2derivative at param, i.e. evaluates slot function L2deriv.fct at param.

L2derivSymm

signature(object = "L2ParamFamily"): accessor function for L2derivSymm.

L2derivDistr

signature(object = "L2ParamFamily"): accessor function for L2derivDistr.

L2derivDistrSymm

signature(object = "L2ParamFamily"): accessor function for L2derivDistrSymm.

FisherInfo

signature(object = "L2ParamFamily"): accessor function for FisherInfo.

FisherInfo

signature(object = "L2ParamFamily", param = "ParamFamParameter"): returns the Fisher Information at param, i.e. evaluates slot function FisherInfo.fct at param.

checkL2deriv

signature(object = "L2ParamFamily"): check centering of L2deriv and compute precision of Fisher information.

E

signature(object = "L2ParamFamily", fun = "EuclRandVariable", cond = "missing"): expectation of fun under the distribution of object.

E

signature(object = "L2ParamFamily", fun = "EuclRandMatrix", cond = "missing"): expectation of fun under the distribution of object.

E

signature(object = "L2ParamFamily", fun = "EuclRandVarList", cond = "missing"): expectation of fun under the distribution of object.

plot

signature(x = "L2ParamFamily"): plot of distribution and L2deriv. More precisely, this method has arguments plot(x, withSweave = getdistrOption("withSweave"), main = FALSE, inner = TRUE, sub = FALSE, col.inner = par("col.main"), cex.inner = 0.8, bmar = par("mar")[1], tmar = par("mar")[3], ..., mfColRow = TRUE, to.draw.arg = NULL, withSubst = TRUE) where

x

object of class "L2ParamFamily"

withSweave

logical: if TRUE (for working with Sweave) no extra device is opened and height/width are not set

main

logical: is a main title to be used? or
just as argument main in plot.default.

inner

logical: do panels have their own titles? or
character vector of / cast to length 'number of plotted panels' with the corresponding panel titles. For further information, see also plot and the description of argument main in plot.default.

sub

logical: is a sub-title to be used? or
just as argument sub in plot.default.

tmar

top margin – useful for non-standard main title sizes

bmar

bottom margin – useful for non-standard sub title sizes

cex.inner

magnification to be used for inner titles relative to the current setting of cex; as in par; can be a vector of length 2; in this case the first component is for the distribution panels, the second for the L2-derivative-panels.

col.inner

character or integer code; color for the inner title

mfColRow

shall default partition in panels be used — defaults to TRUE

to.draw.arg

Either NULL (default; everything is plotted) or a vector of either integers (the indices of the subplots to be drawn) or characters — the names of the subplots to be drawn: these names are to be chosen among c("d","p","q", dimnms) where dimnms is either the row names of the trafo matrix rownames(trafo(x@param)) or if the last expression is NULL a vector "dim<dimnr>", dimnr running through the number of rows of the trafo matrix.

withSubst

logical; if TRUE (default) pattern substitution for titles and lables is used; otherwise no substitution is used.

...

addtional arguments for plot — see plot, plot.default, plot.stepfun

If ... contains argument ylim, this may either be as in plot.default (i.e. a vector of length 2) or a vector of length 4, where the first two elements are the values for ylim in panels "d.c" and "d.d", and the last two elements are the values for ylim resp. xlim in panels "p", "p.c", "p.d" and "q", "q.c", "q.d". In all title and axis label arguments, if withSubst is TRUE, the following patterns are substituted:

"%C"

class of argument x

"%A"

deparsed argument x

"%D"

time/date-string when the plot was generated

In addition, argument ... may contain arguments panel.first, panel.last, i.e., hook expressions to be evaluated at the very beginning and at the very end of each panel (within the then valid coordinates). To be able to use these hooks for each panel individually, they may also be lists of expressions (of the same length as the number of panels and run through in the same order as the panels).

The return value of the plot methods is an S3 object of class c("plotInfo","DiagnInfo"), i.e., a list containing the information needed to produce the respective plot, which at a later stage could be used by different graphic engines (like, e.g. ggplot) to produce the plot in a different framework. A more detailed description will follow in a subsequent version.

modifyModel

signature(model = "L2ParamFamily", param = "ParamFamParameter"): moves the L2-parametric Family model to parameter param

Author(s)

Matthias Kohl [email protected],
Peter Ruckdeschel [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

L2ParamFamily, ParamFamily-class

Examples

F1 <- new("L2ParamFamily")
plot(F1)

## selection of subpanels for plotting
F2 <- L2LocationScaleFamily()
layout(matrix(c(1,2,3,3), nrow=2, byrow=TRUE))
plot(F2,mfColRow = FALSE,
     to.draw.arg=c("p","q","loc"))
plot(F2,mfColRow = FALSE, inner=list("empirical cdf","pseudo-inverse",
     "L2-deriv, loc.part"), to.draw.arg=c("p","q","loc"))

Generating function for L2ScaleFamily-class

Description

Generates an object of class "L2ScaleFamily".

Usage

L2ScaleFamily(scale = 1, loc = 0,  name, centraldistribution = Norm(),
              locscalename = c("loc", "scale"), modParam, LogDeriv,  
              L2derivDistr.0, FisherInfo.0, distrSymm, L2derivSymm, 
              L2derivDistrSymm, trafo, .returnClsName = NULL)

Arguments

scale

positive number: scale parameter of the model

loc

numeric: location parameter of the model

name

character: name of the parametric family.

centraldistribution

object of class "AbscontDistribution": central distribution; we assume from the beginning, that centraldistribution is symmetric about 00

locscalename

a character vector of length 1 or 2 containing the names of the scale resp. of location and scale parameter; if length is 2, locscalename is either unnamed, then order must be c(scale,loc), or named, then names must be "loc" and "scale".

modParam

optional function: mapping from the parameter space (represented by "param") to the distribution space (represented by "distribution").

LogDeriv

function with argument x: the negative logarithmic derivative of the density of the central distribution; if missing, it is determined numerically using numeric differentiation.

L2derivDistr.0

object of class "UnivariateDistribution": distribution of the L2derivative at the central distribution

FisherInfo.0

object of class "PosSemDefSymmMatrix": Fisher information of the model at the "standard" parameter value

distrSymm

object of class "DistributionSymmetry": symmetry of distribution.

L2derivSymm

object of class "FunSymmList": symmetry of the maps contained in L2deriv

L2derivDistrSymm

object of class "DistrSymmList": symmetry of the distributions contained in L2derivDistr

trafo

matrix or function in param: transformation of the parameter

.returnClsName

the class name of the return value; by default this argument is NULL whereupon the return class will be L2ScaleFamily; but, internally, this generating function is also used to produce objects of class NormScaleFamily, ExpScaleFamily, and LnormScaleFamily.

Details

If name is missing, the default “L2 scale family” is used. The function modParam is optional. If it is missing, it is constructed from centraldistribution using the scale structure of the model. Slot param is filled accordingly with the argument trafo passed to L2ScaleFamily. In case L2derivDistr.0 is missing, L2derivDistr is computed via imageDistr, else L2derivDistr is assigned L2derivDistr.0, coerced to "UnivariateDistributionList". In case FisherInfo.0 is missing, Fisher information is computed from L2deriv using E. If distrSymm is missing, it is set to symmetry about loc. If L2derivSymm is missing, it is set to no symmetry, and if L2derivDistrSymm is missing, it is set to no symmetry.

Value

Object of class "L2ScaleFamily"

Author(s)

Matthias Kohl [email protected],
Peter Ruckdeschel [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

L2ScaleFamily-class

Examples

F1 <- L2ScaleFamily()
plot(F1)

L2 differentiable parametric group family

Description

Class of L2 differentiable parametric group families.

Objects from the Class

Objects can be created by calls of the form new("L2ScaleFamily", ...). More frequently they are created via the generating function L2ScaleFamily.

Slots

name

[inherited from class "ProbFamily"] object of class "character": name of the family.

distribution

[inherited from class "ProbFamily"] object of class "Distribution": member of the family.

distrSymm

[inherited from class "ProbFamily"] object of class "DistributionSymmetry": symmetry of distribution.

param

[inherited from class "ParamFamily"] object of class "ParamFamParameter": parameter of the family.

fam.call

[inherited from class "ParamFamily"] object of class "call": call by which parametric family was produced.

makeOKPar

[inherited from class "ParamFamily"] object of class "function": has argument param — the (total) parameter, returns valid parameter; used if optim resp. optimize— try to use “illegal” parameter values; then makeOKPar makes a valid parameter value out of the illegal one.

startPar

[inherited from class "ParamFamily"] object of class "function": has argument x — the data, returns starting parameter for optim resp. optimize— a starting estimator in case parameter is multivariate or a search interval in case parameter is univariate.

modifyParam

[inherited from class "ParamFamily"] object of class "function": mapping from the parameter space (represented by "param") to the distribution space (represented by "distribution").

props

[inherited from class "ProbFamily"] object of class "character": properties of the family.

L2deriv

[inherited from class "L2ParamFamily"] object of class "EuclRandVariable": L2 derivative of the family.

L2deriv.fct

[inherited from class "L2ParamFamily"] object of class "function": mapping from the parameter space (argument param of class "ParamFamParameter") to a mapping from observation x to the value of the L2derivative; L2deriv.fct is then used from observation x to value of the L2derivative; L2deriv.fct is used by modifyModel to move the L2deriv according to a change in the parameter

L2derivSymm

[inherited from class "L2ParamFamily"] object of class "FunSymmList": symmetry of the maps included in L2deriv.

L2derivDistr

[inherited from class "L2ParamFamily"] object of class "UnivarDistrList": list which includes the distribution of L2deriv.

L2derivDistrSymm

[inherited from class "L2ParamFamily"] object of class "DistrSymmList": symmetry of the distributions included in L2derivDistr.

FisherInfo.fct

[inherited from class "L2ParamFamily"] object of class "function": mapping from the parameter space (argument param of class "ParamFamParameter") to the set of positive semidefinite matrices; FisherInfo.fct is used by modifyModel to move the Fisher information according to a change in the parameter

FisherInfo

[inherited from class "L2ParamFamily"] object of class "PosDefSymmMatrix": Fisher information of the family.

LogDeriv

[inherited from class "L2GroupParamFamily"] object of class "function": has argument x; the negative logarithmic derivative of the density of the model distribution at the "standard" parameter value.

locscalename

[inherited from class "L2LocationScaleUnion"] object of class "character": names of location and scale parameter

Extends

Class "L2LocationScaleUnion", directly.
Class "L2GroupParamFamily", by class "L2LocationScaleUnion".
Class "L2ParamFamily", by class "L2GroupParamFamily".
Class "ParamFamily", by class "L2ParamFamily".
Class "ProbFamily", by class "ParamFamily".

Methods

modifyModel

signature(model = "L2ScaleFamily", param = "ParamFamParameter"): moves the L2-scale family model to parameter param

Author(s)

Matthias Kohl [email protected],
Peter Ruckdeschel [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

L2ScaleFamily, ParamFamily-class

Examples

F1 <- new("L2ScaleFamily")
plot(F1)

Generating function for L2LocationScaleFamily-class in nuisance situation

Description

Generates an object of class "L2LocationScaleFamily" in the situation where scale is main, location nuisance parameter.

Usage

L2ScaleUnknownLocationFamily(loc = 0, scale = 1, name, centraldistribution = Norm(),
                      locscalename = c("loc", "scale"), modParam, LogDeriv,  
                      L2derivDistr.0, FisherInfo.0, distrSymm, L2derivSymm, 
                      L2derivDistrSymm, trafo, .returnClsName = NULL)

Arguments

loc

numeric: location parameter of the model.

scale

positive number: scale of the model.

name

character: name of the parametric family.

centraldistribution

object of class "AbscontDistribution": central distribution; we assume by default, that centraldistribution is symmetric about 00

modParam

optional function: mapping from the parameter space (represented by "param") to the distribution space (represented by "distribution").

locscalename

a character vector of length 2 containing the names of the location and scale parameter; either unnamed, then order must be c(loc,scale), or named, then names must be "loc" and "scale"

LogDeriv

function with argument x: the negative logarithmic derivative of the density of the central distribution; if missing, it is determined numerically using numeric differentiation.

L2derivDistr.0

list of length 2 of objects of class "UnivariateDistribution": (marginal) distributions of the coordinates of the L2derivative at the central distribution

FisherInfo.0

object of class "PosSemDefSymmMatrix": Fisher information of the model at the "standard" parameter value

distrSymm

object of class "DistributionSymmetry": symmetry of distribution.

L2derivSymm

object of class "FunSymmList": symmetry of the maps contained in L2deriv

L2derivDistrSymm

object of class "DistrSymmList": symmetry of the distributions contained in L2derivDistr

trafo

matrix or function in param: transformation of the parameter

.returnClsName

the class name of the return value; by default this argument is NULL whereupon the return class will be L2LocationScaleFamily; but, internally, this generating function is also used to produce objects of class NormalLocationScaleFamily, CauchyLocationScaleFamily.

Details

If name is missing, the default “L2 scale family with unknown location (as nuisance)” is used. The function modParam is optional. If it is missing, it is constructed from centraldistribution using the location and scale structure of the model. Slot param is filled accordingly with the argument trafo passed to L2ScaleUnknownLocationFamily. In case L2derivDistr.0 is missing, L2derivDistr is computed via imageDistr, else L2derivDistr is assigned L2derivDistr.0, coerced to "UnivariateDistributionList". In case FisherInfo.0 is missing, Fisher information is computed from L2deriv using E. If distrSymm is missing, it is set to symmetry about loc. If L2derivSymm is missing, its location and scale components are set to no symmetry, respectively. if L2derivDistrSymm is missing, its location and scale components are set to no symmetry, respectively.

Value

Object of class "L2LocationScaleFamily"

Author(s)

Peter Ruckdeschel [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

L2LocationScaleFamily-class

Examples

F1 <- L2ScaleUnknownLocationFamily()
plot(F1)

Generating function for lognormal scale families

Description

Generates an object of class "L2ScaleFamily" which represents a lognormal scale family.

Usage

LnormScaleFamily(meanlog = 0, sdlog = 1, trafo)

Arguments

meanlog

mean of the distribution on the log scale

sdlog

standard deviation of the distribution on the log scale

trafo

matrix: transformation of the parameter

Details

The slots of the corresponding L2 differentiable parameteric family are filled.

Value

Object of class "L2ScaleFamily"

Author(s)

Matthias Kohl [email protected]

References

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

L2ParamFamily-class, Lnorm-class

Examples

(L1 <- LnormScaleFamily())
plot(L1)
Map(L2deriv(L1)[[1]])
checkL2deriv(L1)

Generating function for Logistic location and scale families

Description

Generates an object of class "L2LocationScaleFamily" which represents a normal location and scale family.

Usage

LogisticLocationScaleFamily(location = 0, scale = 1, trafo)
LOGISTINT2

Arguments

location

location

scale

scale

trafo

function in param or matrix: transformation of the parameter

Details

The slots of the corresponding L2 differentiable parameteric family are filled. LOGISTINT2 is a constant used for the scale part of the Fisher information. More precisely LOGISTINT2 equals to (tanh(x/2)x1)2dlogis(x)dx\int_{-\infty}^{\infty} (\tanh(x/2)\,x-1)^2\,{\rm dlogis}(x)\,dx.

Value

Object of class "L2LocationScaleFamily"

Author(s)

Peter Ruckdeschel [email protected]

References

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

L2ParamFamily-class, Logis-class

Examples

(L1 <- LogisticLocationScaleFamily())
## synonymous: L1 <- LogisticFamily()
plot(L1)
FisherInfo(L1)
### need smaller integration range:
distrExoptions("ElowerTruncQuantile"=1e-4,"EupperTruncQuantile"=1e-4)
checkL2deriv(L1)
distrExoptions("ElowerTruncQuantile"=1e-7,"EupperTruncQuantile"=1e-7)
##
set.seed(123)
x <- rlogis(100,location=1,scale=2)
CvMMDEstimator(x, L1)

Methods for functions mceCalc and mleCalc in Package ‘distrMod’

Description

Methods for functions mceCalc and mleCalc in package distrMod;

Usage

mceCalc(x, PFam, ...)
mleCalc(x, PFam, ...)
## S4 method for signature 'numeric,ParamFamily'
mceCalc(x, PFam, criterion, 
                   startPar = NULL, penalty = 1e20, crit.name,
                   Infos = NULL, validity.check = TRUE,
                   withthetaPar = FALSE,...)
## S4 method for signature 'numeric,ParamFamily'
mleCalc(x, PFam, startPar = NULL, 
                   penalty = 1e20, dropZeroDensity = TRUE, Infos = NULL,
                    validity.check = TRUE, ...)
## S4 method for signature 'numeric,BinomFamily'
mleCalc(x, PFam, ...)
## S4 method for signature 'numeric,PoisFamily'
mleCalc(x, PFam, ...)
## S4 method for signature 'numeric,NormLocationFamily'
mleCalc(x, PFam, ...)
## S4 method for signature 'numeric,NormScaleFamily'
mleCalc(x, PFam, ...)
## S4 method for signature 'numeric,NormLocationScaleFamily'
mleCalc(x, PFam, ...)

Arguments

x

numeric; data at which to evaluate the estimator

PFam

an object of class ParamFamily; the parametric family at which to evaluate the estimator

criterion

a function measuring the “goodness of fit”

startPar

in case optim is used: a starting value for the parameter fit; in case optimize is used: a vector containing a search interval for the (one-dim) parameter

penalty

numeric; penalizes non-permitted parameter values

crit.name

character; the name of the criterion; may be missing

withthetaPar

logical; shall Parameter theta be transmitted?

Infos

matrix; info slot to be filled in object of class MCEstimate; may be missing

validity.check

logical: shall return parameter value be checked for validity?

dropZeroDensity

logical of length 1; shall observations with density zero be dropped? Optimizers like optim require finite values, so get problems when negative loglikelihood is evaluated.

...

additional argument(s) for optim / optimize

Details

mceCalc is used internally by function MCEstimator to allow for method dispatch according to argument PFam; similarly, and for the same purpose mleCalc is used internally by function MLEstimator. This way we / or any other developper can write particular methods for special cases where we may avoid using numerical optimization without interfering with existing code. For programming one's own mleCalc / mceCalc methods, there is the helper function meRes to produce consistent return values.

Value

a list with components

estimate

— the estimate as a named vector of numeric

criterion

— the criterion value (i.e.; a numeric of length 1); e.g. the neg. log likelihood

est.name

— the name of the estimator

param

— estimate coerced to class ParamFamParameter

crit.fct

— a function with the named components of theta as arguments returning the criterion value; used for profiling / coercing to class mle

method

— a character reporting how the estimate was obtained, i.e., by optim, by optimize or by explicit calculations

crit.name

character; the name of the criterion; may be ""

Infos

matrix; info slot to be filled in object of class MCEstimate; may be NULL

samplesize

numeric; sample size of x


MCEstimate-class.

Description

Class of minimum criterion estimates.

Objects from the Class

Objects can be created by calls of the form new("MCEstimate", ...). More frequently they are created via the generating functions MCEstimator, MDEstimator or MLEstimator. More specifically, MDEstimator, CvMMDEstimator, and MLEstimator return objects of classes MDEstimate, CvMMDEstimate, and MLEstimate respectively, which each are immediate subclasses of MCEstimate (without further slots, for internal use in method dispatch).

Slots

name

Object of class "character": name of the estimator.

estimate

Object of class "ANY": estimate.

estimate.call

Object of class "call": call by which estimate was produced.

criterion

Object of class "numeric": minimum value of the considered criterion.

criterion.fct

Object of class "function": the considered criterion function; used for compatibility with class "mle" from package stats4; should be a function returning the criterion; i.e. a numeric of length 1 and should have as arguments all named components of argument untransformed.estimate

method

Object of class "character": the method by which the estimate was calculated, i.e.; "optim", "optimize", or "explicit calculation"; used for compatibility with class "mle" from package stats4, could be any character value.

Infos

object of class "matrix" with two columns named method and message: additional informations.

optimwarn

object of class "character" warnings issued during optimization.

optimReturn

object of class "ANY" the return value of the optimizer (or NULL if, e.g., closed form solutions are used).

startPar

— object of class "ANY"; filled either with NULL (no starting value used) or with "numeric" — the value of the starting parameter.

asvar

object of class "OptionalMatrix" which may contain the asymptotic (co)variance of the estimator.

samplesize

object of class "numeric" — the samplesize at which the estimate was evaluated.

nuis.idx

object of class "OptionalNumeric": indices of estimate belonging to the nuisance part

fixed

object of class "OptionalNumeric": the fixed and known part of the parameter.

trafo

object of class "list": a list with components fct and mat (see below).

untransformed.estimate

Object of class "ANY": untransformed estimate.

untransformed.asvar

object of class "OptionalNumericOrMatrix" which may contain the asymptotic (co)variance of the untransformed estimator.

completecases

object of class "logical" — complete cases at which the estimate was evaluated.

startPar

object of class "ANY"; usually filled with argument startPar of generating function MCEstimator, MLEstimator, MDEstimator.

Extends

Class "Estimate", directly.

Methods

criterion

signature(object = "MCEstimate"): accessor function for slot criterion.

criterion<-

signature(object = "MCEstimate"): replacement function for slot criterion.

optimwarn

signature(object = "MCEstimate"): accessor function for slot optimwarn.

optimReturn

signature(object = "MCEstimate"): accessor function for slot optimReturn.

startPar

signature(object = "MCEstimate"): accessor function for slot startPar.

criterion.fct

signature(object = "MCEstimate"): accessor function for slot criterion.fct.

show

signature(object = "Estimate")

coerce

signature(from = "MCEstimate", to = "mle"): create a "mle" object from a "MCEstimate" object

profile

signature(fitted = "MCEstimate"): coerces fitted to class "mle" and then calls the corresponding profile-method from package stats4; for details we confer to the corresponding man page.

Author(s)

Matthias Kohl [email protected],
Peter Ruckdeschel [email protected]

See Also

Estimate-class, MCEstimator, MDEstimator, MLEstimator

Examples

## (empirical) Data
x <- rgamma(50, scale = 0.5, shape = 3)

## parametric family of probability measures
G <- GammaFamily(scale = 1, shape = 2)

MDEstimator(x, G)
(m <- MLEstimator(x, G))
m.mle <- as(m,"mle")
par(mfrow=c(1,2))
profileM <- profile(m)
## plot-profile throws an error

Function to compute minimum criterion estimates

Description

The function MCEstimator provides a general way to compute estimates for a given parametric family of probability measures which can be obtain by minimizing a certain criterion. For instance, the negative log-Likelihood in case of the maximum likelihood estimator or some distance between distributions like in case of minimum distance estimators.

Usage

MCEstimator(x, ParamFamily, criterion, crit.name, 
            startPar = NULL, Infos, trafo = NULL, 
            penalty = 1e20, validity.check = TRUE, asvar.fct, na.rm = TRUE,
            ..., .withEvalAsVar = TRUE, nmsffx = "",
            .with.checkEstClassForParamFamily = TRUE)

Arguments

x

(empirical) data

ParamFamily

object of class "ParamFamily"

criterion

function: criterion to minimize; see Details section.

crit.name

optional name for criterion.

startPar

initial information used by optimize resp. optim; i.e; if (total) parameter is of length 1, startPar is a search interval, else it is an initial parameter value; if NULL slot startPar of ParamFamily is used to produce it; in the multivariate case, startPar may also be of class Estimate, in which case slot untransformed.estimate is used.

Infos

character: optional informations about estimator

trafo

an object of class MatrixorFunction – a transformation for the main parameter

penalty

(non-negative) numeric: penalizes non valid parameter-values

validity.check

logical: shall return parameter value be checked for validity? Defaults to yes (TRUE)

asvar.fct

optionally: a function to determine the corresponding asymptotic variance; if given, asvar.fct takes arguments L2Fam((the parametric model as object of class L2ParamFamily)) and param (the parameter value as object of class ParamFamParameter); arguments are called by name; asvar.fct may also process further arguments passed through the ... argument

na.rm

logical: if TRUE, the estimator is evaluated at complete.cases(x).

...

further arguments to criterion or optimize or optim, respectively.

.withEvalAsVar

logical: shall slot asVar be evaluated (if asvar.fct is given) or just the call be returned?

nmsffx

character: a potential suffix to be appended to the estimator name.

.with.checkEstClassForParamFamily

logical: Should a the end of the function .checkEstClassForParamFamily; defaults to TRUE; can be switched off for computational time or because this is already checked in a calling wrapper function.

Details

The argument criterion has to be a function with arguments the empirical data as well as an object of class "Distribution" and possibly .... Uses mceCalc for method dispatch.

Value

An object of S4-class "MCEstimate" which inherits from class "Estimate".

Note

The criterion function may be called together with a parameter thetaPar which is the current parameter value under consideration, i.e.; the value under which the model distribution is considered. Hence, if desired, particular criterion functions could make use of this information, by, say computing the criterion differently for different parameter values.

Author(s)

Matthias Kohl [email protected],
Peter Ruckdeschel [email protected]

See Also

ParamFamily-class, ParamFamily, MCEstimate-class

Examples

## (empirical) Data
x <- rgamma(50, scale = 0.5, shape = 3)

## parametric family of probability measures
G <- GammaFamily(scale = 1, shape = 2)

## Maximum Likelihood estimator
## Note: you can directly use function MLEstimator!
negLoglikelihood <- function(x, Distribution){
    res <- -sum(log(Distribution@d(x)))
    names(res) <- "Negative Log-Likelihood"
    return(res)
}
MCEstimator(x = x, ParamFamily = G, criterion = negLoglikelihood)

## Kolmogorov(-Smirnov) minimum distance estimator
## Note: you can also use function MDEstimator!
MCEstimator(x = x, ParamFamily = G, criterion = KolmogorovDist, 
            crit.name = "Kolmogorov distance")

## Total variation minimum distance estimator
## Note: you can also use function MDEstimator!
## discretize Gamma distribution

## IGNORE_RDIFF_BEGIN
MCEstimator(x = x, ParamFamily = G, criterion = TotalVarDist,
            crit.name = "Total variation distance")
## IGNORE_RDIFF_END

## or smooth empirical distribution (takes some time!)
#MCEstimator(x = x, ParamFamily = G, criterion = TotalVarDist, 
#            asis.smooth.discretize = "smooth", crit.name = "Total variation distance")

## Hellinger minimum distance estimator
## Note: you can also use function MDEstimator!
## discretize Gamma distribution
distroptions(DistrResolution = 1e-8)
MCEstimator(x = x, ParamFamily = G, criterion = HellingerDist, 
            crit.name = "Hellinger Distance", startPar = c(1,2))
distroptions(DistrResolution = 1e-6)

## or smooth empirical distribution (takes some time!)
#MCEstimator(x = x, ParamFamily = G, criterion = HellingerDist, 
#            asis.smooth.discretize = "smooth", crit.name = "Hellinger distance")

Function to compute minimum distance estimates

Description

The function MDEstimator provides a general way to compute minimum distance estimates.

Usage

MDEstimator(x, ParamFamily, distance = KolmogorovDist, dist.name, 
            paramDepDist = FALSE, startPar = NULL, Infos, trafo = NULL,
            penalty = 1e20, validity.check = TRUE, asvar.fct, na.rm = TRUE,
            ..., .withEvalAsVar = TRUE, nmsffx = "",
            .with.checkEstClassForParamFamily = TRUE)
CvMMDEstimator(x, ParamFamily, muDatOrMod = c("Mod","Dat", "Other"),
            mu = NULL, paramDepDist = FALSE, startPar = NULL, Infos,
            trafo = NULL, penalty = 1e20, validity.check = TRUE, 
            asvar.fct = .CvMMDCovariance, na.rm = TRUE, ...,
            .withEvalAsVar = TRUE, nmsffx = "",
            .with.checkEstClassForParamFamily = TRUE)
KolmogorovMDEstimator(x, ParamFamily, paramDepDist = FALSE, startPar = NULL, Infos, 
            trafo = NULL, penalty = 1e20, validity.check = TRUE, asvar.fct, 
            na.rm = TRUE, ..., .withEvalAsVar = TRUE, nmsffx = "",
            .with.checkEstClassForParamFamily = TRUE)
TotalVarMDEstimator(x, ParamFamily, paramDepDist = FALSE, startPar = NULL, Infos, 
            trafo = NULL, penalty = 1e20, validity.check = TRUE, asvar.fct, 
            na.rm = TRUE, ..., .withEvalAsVar = TRUE, nmsffx = "",
            .with.checkEstClassForParamFamily = TRUE)
HellingerMDEstimator(x, ParamFamily, paramDepDist = FALSE, startPar = NULL, Infos, 
            trafo = NULL, penalty = 1e20, validity.check = TRUE, asvar.fct, 
            na.rm = TRUE, ..., .withEvalAsVar = TRUE, nmsffx = "",
            .with.checkEstClassForParamFamily = TRUE)
CvMDist2(e1,e2,... )

Arguments

x

(empirical) data

ParamFamily

object of class "ParamFamily"

distance

(generic) function: to compute distance beetween (emprical) data and objects of class "Distribution".

dist.name

optional name of distance

muDatOrMod

a character string specifying whether as integration measure mumu in Cramer-von-Mises distance, the empirical cdf (corresponding to argument value "Dat") or the current model distribution (corresponding to argument value "Mod") or a given integration (probability) measure / distribution mu (corresponding to argument value "Other") is to be used; must be one of "Dat" (default) or "Mod" or "Other". You can specify just the initial letter; the default is "Mod".

mu

optional integration (probability) measure for CvM MDE. defaults to NULL and is ignored in options muDatOrMod in "Dat" and "Mod"; in case "Other", it must be of class UnivariateDistribution.

paramDepDist

logical; will computation of distance be parameter dependent (see also note below)? if TRUE, distance function must be able to digest a parameter thetaPar; otherwise this parameter will be eliminated if present in ...-argument.

startPar

initial information used by optimize resp. optim; i.e; if (total) parameter is of length 1, startPar is a search interval, else it is an initial parameter value; if NULL slot startPar of ParamFamily is used to produce it; in the multivariate case, startPar may also be of class Estimate, in which case slot untransformed.estimate is used.

Infos

character: optional informations about estimator

trafo

an object of class MatrixorFunction – a transformation for the main parameter

penalty

(non-negative) numeric: penalizes non valid parameter-values

validity.check

logical: shall return parameter value be checked for validity? Defaults to yes (TRUE)

asvar.fct

optionally: a function to determine the corresponding asymptotic variance; if given, asvar.fct takes arguments L2Fam((the parametric model as object of class L2ParamFamily)) and param (the parameter value as object of class ParamFamParameter); arguments are called by name; asvar.fct may also process further arguments passed through the ... argument

na.rm

logical: if TRUE, the estimator is evaluated at complete.cases(x).

...

for the estimators: further arguments to criterion or optimize or optim, respectively; for CvMDist2, these can be used e.g. by E().

.withEvalAsVar

logical: shall slot asVar be evaluated (if asvar.fct is given) or just the call be returned?

nmsffx

character: a potential suffix to be appended to the estimator name.

e1

object of class "Distribution" or class "numeric"

e2

object of class "Distribution"

.with.checkEstClassForParamFamily

logical: Should a the end of the function .checkEstClassForParamFamily; defaults to TRUE; can be switched off for computational time or because this is already checked in a calling wrapper function.

Details

The argument distance has to be a (generic) function with arguments the empirical data as well as an object of class "Distribution" and possibly ...; e.g. KolmogorovDist (default), TotalVarDist or HellingerDist. Uses mceCalc for method dispatch.

The functions CvMMDEstimator, KolmogorovMDEstimator, TotalVarMDEstimator, and HellingerMDEstimator are aliases where the distance is fixed. More specifically, CvMMDEstimator uses Cramer-von-Mises distance, see CvMDist with integration measure mumu either equal to the empirical cdf or to the current best fitting model distribution; the alternative is selected by argument muDatOrMod). As it is asymptotically linear, asymptotic variances are available. In case of alternative "Dat", this variance is computed by means of helper function .CvMMDCovarianceWithMux, case of alternative "Mod" we use helper function .CvMMDCovariance. In both case one may use these helper function to get hand on the respective influence function. For covariances computed by .CvMMDCovariance, diagnostics on the involved integrations are available if argument diagnostic is TRUE. Then there is attribute diagnostic attached to the return value, which may be inspected and accessed through showDiagnostic and getDiagnostic.

KolmogorovMDEstimator uses Kolmogorov distance, see KolmogorovDist, TotalVarMDEstimator, uses total variation distance, see TotalVarDist and HellingerMDEstimator uses Hellinger distance, see HellingerDist.

Function CvMDist2 calls CvMDist and computes the Cramer-von-Mises distance between distributions e1 and e2 with integration measure mu equal to e2; it is used in alternative "Mod" in CvMMDEstimator.

Value

The estimators return an object of S4-class "MCEstimate" which inherits from class "Estimate". CvMDist2 returns the respective distance.

Theoretical Background

It should be noted that CvMMDEstimator results in an asymptotically linear (hence asymptotically normal) estimator with an influence function which is always bounded; HellingerMDEstimator adapts, for growing sample size, the MLE estimator, hence is asymptotically efficient, while for finite sample size is bias robust. KolmogorovMDEstimator is square-root-n consistent but, due to the facetted level sets of the distance fails to be asymptotically normal. In the terminology of Donoho/Liu, TotalVarMDEstimator and HellingerMDEstimator rely on strong distances, while CvMMDEstimator and KolmogorovMDEstimator use weak distances, so the latter ensure protection against larger classes of contamination (simply because the distribution balls based on the respective distances contain more elements).

Note

The distance function may be called together with a parameter thetaPar which is the current parameter value under consideration, i.e.; the value under which the model distribution is considered. Hence, if desired, particular distance functions could make use of this information, by, say computing the distance differently for different parameter values.

Author(s)

Matthias Kohl [email protected],
Peter Ruckdeschel [email protected]

References

Beran, R. (1977). Minimum Hellinger distance estimates for parametric models. Annals of Statistics, 5(3), 445-463.

Donoho, D.L. and Liu, R.C. (1988). The "automatic" robustness of minimum distance functionals. Annals of Statistics, 16(2), 552-586.

Huber, P.J. (1981) Robust Statistics. New York: Wiley.

Parr, W.C. and Schucany, W.R. (1980). Minimum distance and robust estimation. Journal of the American Statistical Association, 75(371), 616-624.

Rao, P.V., Schuster, E.F., and Littell, R.C. (1975). Estimation of Shift and Center of Symmetry Based on Kolmogorov-Smirnov Statistics. Annals of Statistics, 3, 862-873.

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

See Also

ParamFamily-class, ParamFamily, MCEstimator, MCEstimate-class, fitdistr

Examples

## (empirical) Data
set.seed(123)
x <- rgamma(50, scale = 0.5, shape = 3)

## parametric family of probability measures
G <- GammaFamily(scale = 1, shape = 2)

## Kolmogorov(-Smirnov) minimum distance estimator
MDEstimator(x = x, ParamFamily = G, distance = KolmogorovDist)
## or
KolmogorovMDEstimator(x = x, ParamFamily = G)

## von Mises minimum distance estimator with default mu = Mod
MDEstimator(x = x, ParamFamily = G, distance = CvMDist)


### these examples take too much time for R CMD check --as-cran

## von Mises minimum distance estimator with default mu = Mod
MDEstimator(x = x, ParamFamily = G, distance = CvMDist,
            asvar.fct = .CvMMDCovarianceWithMux)
## or
CvMMDEstimator(x = x, ParamFamily = G)
## or
CvMMDEstimator(x = x, ParamFamily = G, muDatOrMod="Mod")

## or with data based integration measure:
CvMMDEstimator(x = x, ParamFamily = G, muDatOrMod="Dat")

## von Mises minimum distance estimator with mu = N(0,1)
MDEstimator(x = x, ParamFamily = G, distance = CvMDist, mu = Norm())
## or, with asy Var
MDEstimator(x = x, ParamFamily = G, distance = CvMDist, mu = Norm(),
            asvar.fct = function(L2Fam, param, ...){
            .CvMMDCovariance(L2Fam=L2Fam, param=param, mu=Norm(), N = 400)
            } )
## synomymous to
CvMMDEstimator(x = x, ParamFamily = G, muDatOrMod="Other", mu = Norm())

## Total variation minimum distance estimator
## gamma distributions are discretized
MDEstimator(x = x, ParamFamily = G, distance = TotalVarDist)
## or
TotalVarMDEstimator(x = x, ParamFamily = G)
## or smoothing of emprical distribution (takes some time!)
#MDEstimator(x = x, ParamFamily = G, distance = TotalVarDist, asis.smooth.discretize = "smooth")

## Hellinger minimum distance estimator
## gamma distributions are discretized
distroptions(DistrResolution = 1e-10)
MDEstimator(x = x, ParamFamily = G, distance = HellingerDist, startPar = c(1,2))
## or
HellingerMDEstimator(x = x, ParamFamily = G, startPar = c(1,2))
distroptions(DistrResolution = 1e-6) # default
## or smoothing of emprical distribution (takes some time!)
MDEstimator(x = x, ParamFamily = G, distance = HellingerDist, asis.smooth.discretize = "smooth")

helper functions for mceCalc and mleCalc

Description

helper functions to produce consistent lists to be digested in functions mceCalc and mleCalc

Usage

meRes(x, estimate, criterion.value, param, crit.fct, method = "explicit solution",
      crit.name = "Maximum Likelihood", Infos, warns = "", startPar = NULL,
      optReturn = NULL)
get.criterion.fct(theta, Data, ParamFam, criterion.ff, fun, ...)
## S4 method for signature 'numeric'
samplesize(object)

Arguments

x

numeric; the data at which to evaluate the estimate

estimate

numeric; the estimate

criterion.value

numeric; the value of the criterion

param

object of class ParamFamParameter; the parameter value

crit.fct

a function to fill slot minuslogl when an object of class MCEstimate is coerced to class mle (from package stats4); to this end function get.criterion.fct (also see details below) is helpful (at least if the dimension of the estimator is larger than 1).

method

character; describes how the estimate was obtained

crit.name

character; name of the criterion

Infos

optional matrix of characters in two columns; information to be attached to the estimate

warns

collected warnings in optimization

samplesize

numeric; the sample size at which the estimator was evaluated

theta

the parameter value as named numeric vector

Data

numeric; the data at which to evaluate the MCE

ParamFam

an object of class ParamFamily; the parametric family at which to evaluate the MCE

criterion.ff

the criterion function used in the MCE

fun

wrapper to the criterion function used in the MCE (with certain checking whether parameter value is permitted and possibly penalizing if not; see code to , for example.)

startPar

value of argument StartPar — starting parameter used.

optReturn

object of class "ANY" the return value of the optimizer (or NULL if, e.g., closed form solutions are used).

...

further arguments to be passed to optim / optimize

object

numeric; the data at which to evaluate the estimate

Details

get.criterion.fct produces a function criterion.fct to fill slot minuslogl when an object of class MCEstimate is coerced to class mle (from package stats4); this way we may use profiling methods introduced there also for objects of our classes. More specifically, we produce a function where all coordinates/components of theta appear as separate named arguments, which then calls fun with these separate arguments again stacked to one (named) vector argument;

samplesize determines the samplesize of argument object,i.e.; if object has an attribute dim, it returns dim(object)[2], else length(object).

Value

meRes

a list of prescribed structure to be digested in functions mceCalc and mleCalc by the internal helper function .process.meCalcRes.

get.criterion.fct

a function; see details below;

samplesize

numeric

Author(s)

Peter Ruckdeschel [email protected]


Function to compute maximum likelihood estimates

Description

The function MLEstimator provides a general way to compute maximum likelihood estimates for a given parametric family of probability measures. This is done by calling the function MCEstimator which minimizes the negative log-Likelihood.

Usage

MLEstimator(x, ParamFamily, startPar = NULL, 
            Infos, trafo = NULL, penalty = 1e20,
            validity.check = TRUE, na.rm = TRUE, ...,
            .withEvalAsVar = TRUE, dropZeroDensity = TRUE, nmsffx = "",
            .with.checkEstClassForParamFamily = TRUE)

Arguments

x

(empirical) data

ParamFamily

object of class "ParamFamily"

startPar

initial information used by optimize resp. optim; i.e; if (total) parameter is of length 1, startPar is a search interval, else it is an initial parameter value; if NULL slot startPar of ParamFamily is used to produce it; in the multivariate case, startPar may also be of class Estimate, in which case slot untransformed.estimate is used.

Infos

character: optional informations about estimator

trafo

an object of class MatrixorFunction – a transformation for the main parameter

penalty

(non-negative) numeric: penalizes non valid parameter-values

validity.check

logical: shall return parameter value be checked for validity? Defaults to yes (TRUE)

na.rm

logical: if TRUE, the estimator is evaluated at complete.cases(x).

...

further arguments to criterion or optimize or optim, respectively.

.withEvalAsVar

logical: shall slot asVar be evaluated (if asvar.fct is given) or just the call be returned?

dropZeroDensity

logical of length 1; shall observations with density zero be dropped? Optimizers like optim require finite values, so get problems when negative loglikelihood is evaluated.

nmsffx

character: a potential suffix to be appended to the estimator name.

.with.checkEstClassForParamFamily

logical: Should a the end of the function .checkEstClassForParamFamily; defaults to TRUE; can be switched off for computational time or because this is already checked in a calling wrapper function.

Details

The function uses mleCalc for method dispatch; this method by default calls mceCalc using the negative log-likelihood as criterion which should be minimized.

Value

An object of S4-class "MCEstimate" which inherits from class "Estimate".

Author(s)

Matthias Kohl [email protected],
Peter Ruckdeschel [email protected]

See Also

ParamFamily-class, ParamFamily, MCEstimator, MCEstimate-class, fitdistr, mle

Examples

#############################
## 1. Binomial data
#############################
## (empirical) data
# seed for reproducibility:
set.seed(20200306)
x <- rbinom(100, size=25, prob=.25)

## ML-estimate
MLEstimator(x, BinomFamily(size = 25))


#############################
## 2. Poisson data
#############################
## Example: Rutherford-Geiger (1910); cf. Feller~(1968), Section VI.7 (a)
x <- c(rep(0, 57), rep(1, 203), rep(2, 383), rep(3, 525), rep(4, 532), 
       rep(5, 408), rep(6, 273), rep(7, 139), rep(8, 45), rep(9, 27), 
       rep(10, 10), rep(11, 4), rep(12, 0), rep(13, 1), rep(14, 1))

## ML-estimate
MLEstimator(x, PoisFamily())


#############################
## 3. Normal (Gaussian) location and scale
#############################
## (empirical) data
# seed for reproducibility:
set.seed(20200306)
x <- rnorm(100)

## ML-estimate
MLEstimator(x, NormLocationScaleFamily())
## compare:
c(mean(x),sd(x))


#############################
## 4. Gamma model
#############################
## (empirical) data
# seed for reproducibility:
set.seed(20200306)
x <- rgamma(50, scale = 0.5, shape = 3)

## parametric family of probability measures
G <- GammaFamily(scale = 1, shape = 2)

## Maximum likelihood estimator
(res <- MLEstimator(x = x, ParamFamily = G))

## Asymptotic (CLT-based) confidence interval
confint(res)

## some profiling
par(mfrow=c(1,2))
plot(profile(res))
par(mfrow=c(1,1))

## implementation of ML-estimator of package MASS
require(MASS)
(res1 <- fitdistr(x, "gamma"))

## comparison
## shape
estimate(res)[2]
## rate
1/estimate(res)[1]

## minor differences due to the fact that by default, fitdistr uses
## BFGS, while we use Nelder-Mead instead

## log-likelihood
res1$loglik
## negative log-likelihood
criterion(res)


## explicitely transforming to
## MASS parametrization:
mtrafo <- function(x){
     nms0 <- names(c(main(param(G)),nuisance(param(G))))
     nms <- c("shape","rate")
     fval0 <- c(x[2], 1/x[1])
     names(fval0) <- nms
     mat0 <- matrix( c(0, -1/x[1]^2, 1, 0), nrow = 2, ncol = 2,
                     dimnames = list(nms,nms0))                          
     list(fval = fval0, mat = mat0)}

G2 <- G
trafo(G2) <- mtrafo
res2 <- MLEstimator(x = x, ParamFamily = G2)

old <- getdistrModOption("show.details")
distrModoptions("show.details" = "minimal")
res1
res2

## some profiling
par(mfrow=c(1,2))
plot(profile(res2))
par(mfrow=c(1,1))

#############################
## 5. Cauchy Location Scale model
#############################
(C <- CauchyLocationScaleFamily())
loc.true <- 1
scl.true <- 2

## (empirical) data
# seed for reproducibility:
set.seed(20200306)
x <- rcauchy(50, location = loc.true, scale = scl.true)

## Maximum likelihood estimator
(res <- MLEstimator(x = x, ParamFamily = C))
## Asymptotic (CLT-based) confidence interval
confint(res)

Methods for function modifyModel in Package ‘distrMod’

Description

Methods for function modifyModel in package distrMod; modifyModel moves a model from one parameter value to another.

Usage

modifyModel(model, param,...)
## S4 method for signature 'ParamFamily,ParamFamParameter'
modifyModel(model,param, 
                       .withCall = TRUE, ...)
## S4 method for signature 'L2ParamFamily,ParamFamParameter'
modifyModel(model,param, 
                       .withCall = TRUE, .withL2derivDistr = TRUE, ...)
## S4 method for signature 'L2LocationFamily,ParamFamParameter'
modifyModel(model,param, ...)
## S4 method for signature 'L2ScaleFamily,ParamFamParameter'
modifyModel(model,param, ...)
## S4 method for signature 'L2LocationScaleFamily,ParamFamParameter'
modifyModel(model,
                       param, ...)
## S4 method for signature 'GammaFamily,ParamFamParameter'
modifyModel(model,param, ...)
## S4 method for signature 'ExpScaleFamily,ParamFamParameter'
modifyModel(model,param, ...)

Arguments

model

an object of class ParamFamily — the model to move.

param

an object of class ParamFamParameter — the parameter to move to.

.withCall

logical: shall slot fam.call be updated?

.withL2derivDistr

logical: shall slot L2derivDistr be updated or just the call to do the updated be stored?

...

additional argument(s) for methods; not used so far

Details

modifyModel is merely used internally for moving the model along modified parameter values during a model fit.

It generally simply copies the original model and only modifies the affected slots, i.e. distribution, the distribution of the observations, param, the parameter, L2deriv, the L2-derivative at the parameter, L2FisherInfo, the Fisher information at the parameter, the symmetry slots distrSymm, L2derivSymm, and L2derivDistrSymm, and, finally, L2derivDistr the (marginal) distribution(s) of the L2derivative. By default, also slot fam.call is updated.

In case model is of class L2LocationFamily, L2ScaleFamily, or L2LocationScaleFamily, symmetry slots are updated to be centered about the median of the (central) distribution (assuming the latter is symmetric about the median); as an intermediate step, these methods call the general modifyModel-method for signature L2ParamFamily; in this call, however, slot fam.call is not updated (this is the reason for argument .withCall); this is then done in the individual parts of the corresponding method.

Value

a corresponding instance of the model in argument model with moved parameters.


Generating function for Nbinomial families

Description

Generates an object of class "L2ParamFamily" which represents a Nbinomial family where the probability of success is the parameter of interest.

Usage

NbinomFamily(size = 1, prob = 0.5, trafo)
NbinomwithSizeFamily(size = 1, prob = 0.5, trafo, withL2derivDistr = TRUE)
NbinomMeanSizeFamily(size = 1, mean = 0.5, trafo, withL2derivDistr = TRUE )

Arguments

size

number of trials

prob

probability of success

mean

alternative parameter for negative binomial parameter

trafo

function in param or matrix: transformation of the parameter

withL2derivDistr

logical: shall the distribution of the L2 derivative be computed? Defaults to TRUE; setting it to FALSE speeds up computations.

Details

The slots of the corresponding L2 differentiable parameteric family are filled. NbinomFamily assumes size to be known; while for NbinomwithSizeFamily it is a second (unknown) parameter; for NbinomMeanSizeFamily is like NbinomwithSizeFamily but uses the size,mean parametrization instead of the size,prob one.

Value

Object of class "L2ParamFamily"

Author(s)

Peter Ruckdeschel [email protected]

References

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

Kohl, M. and Ruckdeschel, P. (2010). R Package distrMod: S4 Classes and Methods for Probability Models. To appear in Journal of Statistical Software.

See Also

L2ParamFamily-class, Nbinom-class

Examples

(N1 <- NbinomFamily(size = 25, prob = 0.25))
plot(N1)
FisherInfo(N1)
checkL2deriv(N1)
(N1.w <- NbinomwithSizeFamily(size = 25, prob = 0.25))
plot(N1.w)
FisherInfo(N1.w)
checkL2deriv(N1.w)
(N2.w <- NbinomMeanSizeFamily(size = 25, mean = 75))
plot(N2.w)
FisherInfo(N2.w)
checkL2deriv(N2.w)

Generating function for onesidedBias-class

Description

Generates an object of class "onesidedBias".

Usage

negativeBias(name = "negative Bias")

Arguments

name

name of the bias type

Value

Object of class "onesidedBias"

Author(s)

Peter Ruckdeschel [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Ruckdeschel, P. (2005) Optimally One-Sided Bounded Influence Curves. Mathematical Methods in Statistics 14(1), 105-131.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

onesidedBias-class

Examples

negativeBias()

## The function is currently defined as
function(){ new("onesidedBias", name = "negative Bias", sign = -1) }

Generating function for NonSymmetric-class

Description

Generates an object of class "NonSymmetric".

Usage

NonSymmetric()

Value

Object of class "NonSymmetric"

Author(s)

Matthias Kohl [email protected]

See Also

NonSymmetric-class, FunctionSymmetry-class

Examples

NonSymmetric()

## The function is currently defined as
function(){ new("NonSymmetric") }

Class for Non-symmetric Functions

Description

Class for non-symmetric functions.

Objects from the Class

Objects can be created by calls of the form new("NonSymmetric"). More frequently they are created via the generating function NonSymmetric.

Slots

type

Object of class "character": contains “non-symmetric function”

SymmCenter

Object of class "NULL"

Extends

Class "FunctionSymmetry", directly.
Class "Symmetry", by class "FunctionSymmetry".

Author(s)

Matthias Kohl [email protected]

See Also

NonSymmetric

Examples

new("NonSymmetric")

Norm functions

Description

Functions to determine certain norms.

Usage

EuclideanNorm(x)
QuadFormNorm(x,A)

Arguments

x

vector or matrix; norm is determined columnwise

A

pos. semidefinite Matrix

Value

the columnwise evaluated norms

Author(s)

Peter Ruckdeschel [email protected]

See Also

onesidedBias-class

Examples

mm <- matrix(rnorm(20),2,10)
EuclideanNorm(mm)
QuadFormNorm(mm, A = PosSemDefSymmMatrix(matrix(c(3,1,1,1),2,2)))

Generating function for normal location families

Description

Generates an object of class "L2LocationFamily" which represents a normal location family.

Usage

NormLocationFamily(mean = 0, sd = 1, trafo)

Arguments

mean

mean

sd

standard deviation

trafo

function in param or matrix: transformation of the parameter

Details

The slots of the corresponding L2 differentiable parameteric family are filled.

Value

Object of class "L2LocationFamily"

Author(s)

Matthias Kohl [email protected]

References

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

L2ParamFamily-class, Norm-class

Examples

(N1 <- NormLocationFamily())
plot(N1)
L2derivDistr(N1)

Generating function for normal location and scale families

Description

Generates an object of class "L2LocationScaleFamily" which represents a normal location and scale family.

Usage

NormLocationScaleFamily(mean = 0, sd = 1, trafo)

Arguments

mean

mean

sd

standard deviation

trafo

function in param or matrix: transformation of the parameter

Details

The slots of the corresponding L2 differentiable parameteric family are filled.

Value

Object of class "L2LocationScaleFamily"

Author(s)

Matthias Kohl [email protected]

References

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

L2ParamFamily-class, Norm-class

Examples

(N1 <- NormLocationScaleFamily())
## synonymous: N1 <- NormFamily()
plot(N1)
FisherInfo(N1)
checkL2deriv(N1)

Generating function for normal location families with unknown scale as nuisance

Description

Generates an object of class "L2LocationScaleFamily" which represents a normal location family with unknown scale as nuisance.

Usage

NormLocationUnknownScaleFamily(mean = 0, sd = 1, trafo)

Arguments

mean

mean

sd

standard deviation

trafo

function in param or matrix: transformation of the parameter

Details

The slots of the corresponding L2 differentiable parameteric family are filled.

Value

Object of class "L2LocationScaleFamily"

Author(s)

Matthias Kohl [email protected]

References

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

L2ParamFamily-class, Norm-class

Examples

(N1 <- NormLocationUnknownScaleFamily())
plot(N1)
FisherInfo(N1)
checkL2deriv(N1)

Generating function for normal scale families

Description

Generates an object of class "L2ScaleFamily" which represents a normal scale family.

Usage

NormScaleFamily(sd = 1, mean = 0, trafo)

Arguments

sd

standard deviation

mean

mean

trafo

function in param or matrix: transformation of the parameter

Details

The slots of the corresponding L2 differentiable parameteric family are filled.

Value

Object of class "L2ScaleFamily"

Author(s)

Matthias Kohl [email protected]

References

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

L2ParamFamily-class, Norm-class

Examples

(N1 <- NormScaleFamily())
plot(N1)
FisherInfo(N1)
checkL2deriv(N1)

Generating function for normal scale families with unknown location as nuisance

Description

Generates an object of class "L2LocationScaleFamily" which represents a normal scale family with unknown location as nuisance.

Usage

NormScaleUnknownLocationFamily(sd = 1, mean = 0, trafo)

Arguments

mean

mean

sd

standard deviation

trafo

function in param or matrix: transformation of the parameter

Details

The slots of the corresponding L2 differentiable parameteric family are filled.

Value

Object of class "L2LocationScaleFamily"

Author(s)

Matthias Kohl [email protected]

References

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

L2ParamFamily-class, Norm-class

Examples

(N1 <- NormScaleUnknownLocationFamily())
plot(N1)
FisherInfo(N1)
checkL2deriv(N1)

Generating function for NormType-class

Description

Generates an object of class "NormType".

Usage

NormType(name = "EuclideanNorm", fct = EuclideanNorm)

Arguments

name

slot name of the class

fct

slot fct of the class

Value

Object of class "NormType"

Author(s)

Peter Ruckdeschel [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

NormType-class

Examples

## IGNORE_RDIFF_BEGIN
NormType()
## IGNORE_RDIFF_END

Norm Type

Description

Class of norm types.

Objects from the Class

Could be generated by new("NormType"); more frequently one will use the generating function NormType

Slots

name

Object of class "character".

fct

Object of class "function" — the norm to be evaluated.

Methods

name

signature(object = "NormType"): accessor function for slot name.

name<-

signature(object = "NormType", value = "character"): replacement function for slot name.

fct

signature(object = "NormType"): accessor function for slot fct.

fct<-

signature(object = "NormType", value = "function"): replacement function for slot fct.

Author(s)

Peter Ruckdeschel [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

BiasType-class

Examples

## IGNORE_RDIFF_BEGIN
EuclNorm <- NormType("EuclideanNorm",EuclideanNorm)
fct(EuclNorm)
name(EuclNorm)
## IGNORE_RDIFF_END

Generating function for OddSymmetric-class

Description

Generates an object of class "OddSymmetric".

Usage

OddSymmetric(SymmCenter = 0)

Arguments

SymmCenter

numeric: center of symmetry

Value

Object of class "OddSymmetric"

Author(s)

Matthias Kohl [email protected]

See Also

OddSymmetric-class, FunctionSymmetry-class

Examples

OddSymmetric()

## The function is currently defined as
function(SymmCenter = 0){ 
    new("OddSymmetric", SymmCenter = SymmCenter) 
}

Class for Odd Functions

Description

Class for odd functions.

Objects from the Class

Objects can be created by calls of the form new("OddSymmetric"). More frequently they are created via the generating function OddSymmetric.

Slots

type

Object of class "character": contains “odd function”

SymmCenter

Object of class "numeric": center of symmetry

Extends

Class "FunctionSymmetry", directly.
Class "Symmetry", by class "FunctionSymmetry".

Author(s)

Matthias Kohl [email protected]

See Also

OddSymmetric, FunctionSymmetry-class

Examples

new("OddSymmetric")

onesided Bias Type

Description

Class of onesided bias types.

Objects from the Class

Objects can be created by calls of the form new("onesidedBias", ...). More frequently they are created via the generating function positiveBias or negativeBias.

Slots

name

Object of class "character".

sign

Object of class "numeric"; to be in {-1,1} — whether bias is to be positive or negative

Methods

sign

signature(object = "onesidedBias"): accessor function for slot sign.

sign<-

signature(object = "onesidedBias", value = "numeric"): replacement function for slot sign.

Extends

Class "BiasType", directly.

Author(s)

Peter Ruckdeschel [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Ruckdeschel, P. (2005) Optimally One-Sided Bounded Influence Curves. Mathematical Methods in Statistics 14(1), 105-131.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

BiasType-class

Examples

positiveBias()
## The function is currently defined as
function(){ new("onesidedBias", name = "positive Bias", sign = 1) }

negativeBias()
## The function is currently defined as
function(){ new("onesidedBias", name = "negative Bias", sign = -1) }

pB <- positiveBias()
sign(pB)
try(sign(pB) <- -2) ## error
sign(pB) <- -1

Generating function for ParamFamily-class

Description

Generates an object of class "ParamFamily".

Usage

ParamFamily(name, distribution = Norm(), distrSymm, modifyParam,
            main = main(param), nuisance = nuisance(param),
            fixed = fixed(param), trafo = trafo(param),
            param = ParamFamParameter(name = paste("Parameter of", 
                          name),  main = main, nuisance = nuisance, 
                                  fixed = fixed, trafo = trafo),
            props = character(0),
            startPar = NULL, makeOKPar = NULL)

Arguments

name

character string: name of family

distribution

object of class "Distribution": member of the family

distrSymm

object of class "DistributionSymmetry": symmetry of distribution.

startPar

startPar is a function in the observations x returning initial information for MCEstimator used by optimize resp. optim; i.e; if (total) parameter is of length 1, startPar returns a search interval, else it returns an initial parameter value.

makeOKPar

makeOKPar is a function in the (total) parameter param; used if optim resp. optimize— try to use “illegal” parameter values; then makeOKPar makes a valid parameter value out of the illegal one; if NULL slot makeOKPar of ParamFamily is used to produce it.

main

numeric vector: main parameter

nuisance

numeric vector: nuisance parameter

fixed

numeric vector: fixed part of the parameter

trafo

function in param or matrix: transformation of the parameter

param

object of class "ParamFamParameter": parameter of the family

modifyParam

function: mapping from the parameter space (represented by "param") to the distribution space (represented by "distribution").

props

character vector: properties of the family

Details

If name is missing, the default “"parametric family of probability measures"” is used. In case distrSymm is missing it is set to NoSymmetry(). If param is missing, the parameter is created via main, nuisance and trafo as described in ParamFamParameter. One has to specify a function which represents a mapping from the parameter space to the corresponding distribution space; e.g., in case of normal location a simple version of such a function would be function(theta){ Norm(mean = theta) }.

Value

Object of class "ParamFamily"

Author(s)

Matthias Kohl [email protected],
Peter Ruckdeschel [email protected]

See Also

ParamFamily-class

Examples

## "default" (normal location)
F1 <- ParamFamily(modifyParam = function(theta){ Norm(mean = theta) })
plot(F1)

################################
## Some examples:
################################
## 1. Normal location family
theta <- 0
names(theta) <- "mean"
NL <- ParamFamily(name = "Normal location family",
          param = ParamFamParameter(name = "location parameter", main = theta),
          distribution = Norm(mean = 0, sd = 1), ## sd known!
          startPar = function(x,...) c(min(x),max(x)),
          distrSymm <- SphericalSymmetry(SymmCenter = 0),
          modifyParam = function(theta){ Norm(mean = theta, sd = 1) },
          props = paste(c("The normal location family is invariant under",
                    "the group of transformations 'g(x) = x + mean'",
                    "with location parameter 'mean'"), collapse = " "))
NL

## 2. Normal scale family
theta <- 1
names(theta) <- "sd"
NS <- ParamFamily(name = "Normal scale family",
          param = ParamFamParameter(name = "scale parameter", main = theta,
          .returnClsName = "ParamWithScaleFamParameter"),
          distribution = Norm(mean = 0, sd = 1), ## mean known!
          startPar = function(x,...) c(0,-min(x)+max(x)),
          distrSymm <- SphericalSymmetry(SymmCenter = 0),
          modifyParam = function(theta){ Norm(mean = 0, sd = theta) },
          props = paste(c("The normal scale family is invariant under",
                    "the group of transformations 'g(y) = sd*y'",
                    "with scale parameter 'sd'"), collapse = " "))
NS

## 3. Normal location and scale family
theta <- c(0, 1)
names(theta) <- c("mean", "sd")
NLS <- ParamFamily(name = "Normal location and scale family",
          param = ParamFamParameter(name = "location and scale parameter",
                                    main = theta,
                                 .returnClsName = "ParamWithScaleFamParameter"),
          distribution = Norm(mean = 0, sd = 1),
          startPar = function(x,...) c(median(x),mad(x)),
          makeOKPar = function(param) {param[2]<-abs(param[2]); return(param)},
          distrSymm <- SphericalSymmetry(SymmCenter = 0),
          modifyParam = function(theta){
                            Norm(mean = theta[1], sd = theta[2])
                        },
          props = paste(c("The normal location and scale family is",
                    "invariant under the group of transformations",
                    "'g(x) = sd*x + mean' with location parameter",
                    "'mean' and scale parameter 'sd'"),
                    collapse = " "))
NLS

## 4. Binomial family
theta <- 0.3
names(theta) <- "prob"
B <- ParamFamily(name = "Binomial family",
         param = ParamFamParameter(name = "probability of success", 
                                   main = theta),
         startPar = function(x,...) c(0,1),
         distribution = Binom(size = 15, prob = 0.3), ## size known!
         modifyParam = function(theta){ Binom(size = 15, prob = theta) },
         props = paste(c("The Binomial family is symmetric with respect",
                   "to prob = 0.5; i.e.,",
                   "d(Binom(size, prob))(k)=d(Binom(size,1-prob))(size-k)"),
                   collapse = " "))
B

## 5. Poisson family
theta <- 7
names(theta) <- "lambda"
P <- ParamFamily(name = "Poisson family",
          param = ParamFamParameter(name = "positive mean", main = theta),
          startPar = function(x,...) c(0,max(x)),
          distribution = Pois(lambda = 7),
          modifyParam = function(theta){ Pois(lambda = theta) })
P


## 6. Exponential scale family
theta <- 2
names(theta) <- "scale"
ES <- ParamFamily(name = "Exponential scale family",
          param = ParamFamParameter(name = "scale parameter", main = theta,
                           .returnClsName = "ParamWithScaleFamParameter"),
          startPar = function(x,...) c(0,max(x)-min(x)),
          distribution = Exp(rate = 1/2),
          modifyParam = function(theta){ Exp(rate = 1/theta) },
          props = paste(c("The Exponential scale family is invariant under",
                    "the group of transformations 'g(y) = scale*y'",
                    "with scale parameter 'scale = 1/rate'"),
                    collapse = " " ))
ES

## 7. Lognormal scale family
theta <- 2
names(theta) <- "scale"
LS <- ParamFamily(name = "Lognormal scale family",
          param = ParamFamParameter(name = "scale parameter", main = theta,
                           .returnClsName = "ParamWithScaleFamParameter"),
          startPar = function(x,...) c(0,max(x)-min(x)),
          distribution = Lnorm(meanlog = log(2), sdlog = 2),## sdlog known!
          modifyParam = function(theta){ 
                            Lnorm(meanlog = log(theta), sdlog = 2) 
                        },
          props = paste(c("The Lognormal scale family is invariant under",
                    "the group of transformations 'g(y) = scale*y'",
                    "with scale parameter 'scale = exp(meanlog)'"),
                    collapse = " "))
LS

## 8. Gamma family
theta <- c(1, 2)
names(theta) <- c("scale", "shape")
G <- ParamFamily(name = "Gamma family",
        param = ParamFamParameter(name = "scale and shape", main = theta,
                           withPosRestr = TRUE,
                           .returnClsName = "ParamWithScaleAndShapeFamParameter"),
        startPar = function(x,...) {E <- mean(x); V <- var(X); c(V/E,E^2/V)},
        makeOKPar = function(param) abs(param),
        distribution = Gammad(scale = 1, shape = 2),
        modifyParam = function(theta){ 
                          Gammad(scale = theta[1], shape = theta[2]) 
                      },
        props = paste(c("The Gamma family is scale invariant via the",
                  "parametrization '(nu,shape)=(log(scale),shape)'"),
                  collapse = " "))
G

Parametric family of probability measures.

Description

Class of parametric families of probability measures.

Objects from the Class

Objects can be created by calls of the form new("ParamFamily", ...). More frequently they are created via the generating function ParamFamily.

Slots

name

[inherited from class "ProbFamily"] object of class "character": name of the family.

distribution

[inherited from class "ProbFamily"] object of class "Distribution": member of the family.

distrSymm

[inherited from class "ProbFamily"] object of class "DistributionSymmetry": symmetry of distribution.

param

object of class "ParamFamParameter": parameter of the family.

fam.call

object of class "call": call by which parametric family was produced.

makeOKPar

object of class "function": has argument param — the (total) parameter, returns valid parameter; used if optim resp. optimize— try to use “illegal” parameter values; then makeOKPar makes a valid parameter value out of the illegal one.

startPar

object of class "function": has argument x — the data, returns starting parameter for optim resp. optimize— a starting estimator in case parameter is multivariate or a search interval in case parameter is univariate.

modifyParam

object of class "function": mapping from the parameter space (represented by "param") to the distribution space (represented by "distribution").

props

[inherited from class "ProbFamily"] object of class "character": properties of the family.

.withMDE

object of class "logical" (of length 1): Tells R how to use the function from slot startPar in case of a kStepEstimator — use it as is or to compute the starting point for a minimum distance estimator which in turn then serves as starting point for roptest / robest (from package ROptEst). If TRUE (default) the latter alternative is used. Ignored if ROptEst is not used.

.withEvalAsVar

object of class "logical" (of length 1): Tells R whether in determining kStepEstimators one evaluates the asymptotic variance or just produces a call to do so.

Extends

Class "ProbFamily", directly.

Methods

main

signature(object = "ParamFamily"): wrapped accessor function for slot main of slot param.

nuisance

signature(object = "ParamFamily"): wrapped accessor function for slot nuisance of slot param.

fixed

signature(object = "ParamFamily"): wrapped accessor function for slot fixed of slot param.

trafo

signature(object = "ParamFamily", param = "missing"): wrapped accessor function for slot trafo of slot param.

param

signature(object = "ParamFamily"): accessor function for slot param.

modifyParam

signature(object = "ParamFamily"): accessor function for slot modifyParam.

fam.call

signature(object = "ParamFamily"): accessor function for slot fam.call.

plot

signature(x = "ParamFamily"): plot of slot distribution.

The return value of the plot method is an S3 object of class c("plotInfo","DiagnInfo"), i.e., a list containing the information needed to produce the respective plot, which at a later stage could be used by different graphic engines (like, e.g. ggplot) to produce the plot in a different framework. A more detailed description will follow in a subsequent version.

show

signature(object = "ParamFamily")

Details for methods 'show', 'print'

Detailedness of output by methods show, print is controlled by the global option show.details to be set by distrModoptions.

As method show is used when inspecting an object by typing the object's name into the console, show comes without extra arguments and hence detailedness must be controlled by global options.

Method print may be called with a (partially matched) argument show.details, and then the global option is temporarily set to this value.

For class ParamFamily, this becomes relevant for slot param. For details therefore confer to ParamFamParameter-class.

Author(s)

Matthias Kohl [email protected]

See Also

Distribution-class

Examples

F1 <- new("ParamFamily") # prototype
plot(F1)

Generating function for ParamFamParameter-class

Description

Generates an object of class "ParamFamParameter".

Usage

ParamFamParameter(name, main = numeric(0), nuisance, fixed, trafo,
                  ..., .returnClsName = NULL)

Arguments

name

(optional) character string: name of parameter

main

numeric vector: main parameter

nuisance

(optional) numeric vector: nuisance paramter

fixed

(optional) numeric vector: fixed part of the paramter

trafo

(optional) MatrixorFunction: transformation of the parameter

...

(optional) additional arguments for further return classes, e.g.\ withPosRestr (only use case so far) for class ParamWithShapeFamParameter

.returnClsName

character or NULL; if non-null, the generated object will be of class .returnClsName, which must be a subclass of ParamFamParameter.

Details

If name is missing, the default “"parameter of a parametric family of probability measures"” is used. If nuisance is missing, the nuisance parameter is set to NULL. The number of columns of trafo have to be equal and the number of rows have to be not larger than the sum of the lengths of main and nuisance. If trafo is missing, no transformation to the parameter is applied; i.e., trafo is set to an identity matrix.

Value

Object of class "ParamFamParameter" (or, if non-null, of class .returnClsName)

Author(s)

Matthias Kohl [email protected],
Peter Ruckdeschel [email protected]

See Also

ParamFamParameter-class

Examples

ParamFamParameter(main = 0, nuisance = 1, fixed = 2,
                  trafo = function(x) list(fval = sin(x), 
                                            mat = matrix(cos(x),1,1))
                  )

Parameter of a parametric family of probability measures

Description

Class of the parameter of parametric families of probability measures.

Objects from the Class

Objects can be created by calls of the form new("ParamFamParameter", ...). More frequently they are created via the generating function ParamFamParameter.

Slots

main

Object of class "numeric": main parameter.

nuisance

Object of class "OptionalNumeric": optional nuisance parameter.

fixed

Object of class "OptionalNumeric": optional fixed part of the parameter.

trafo

Object of class "MatrixorFunction": transformation of the parameter.

name

Object of class "character": name of the parameter.

withPosRestr

(for ParamWithShapeFamParameter and ParamWithScaleAndShapeFamParameter): Object of class "logical": Is shape restricted to be positive?

Extends

Class "Parameter", directly.
Class "OptionalParameter", by class "Parameter".

Methods

main

signature(object = "ParamFamParameter"): accessor function for slot main.

main<-

signature(object = "ParamFamParameter"): replacement function for slot main.

nuisance

signature(object = "ParamFamParameter"): accessor function for slot nuisance.

nuisance<-

signature(object = "ParamFamParameter"): replacement function for slot nuisance.

fixed

signature(object = "ParamFamParameter"): accessor function for slot fixed.

fixed<-

signature(object = "ParamFamParameter"): replacement function for slot fixed.

trafo

signature(object = "ParamFamParameter"): accessor function for slot trafo.

trafo<-

signature(object = "ParamFamParameter"): replacement function for slot trafo.

length

signature(x = "ParamFamParameter"): sum of the lengths of main and nuisance.

dimension

signature(x = "ParamFamParameter"): length of main.

withPosRestr

signature(object = "ParamWithShapeFamParameter"): accessor function for slot trafo.

withPosRestr<-

signature(object = "ParamWithShapeFamParameter"): replacement function for slot trafo.

show

signature(object = "ParamFamParameter")

show

signature(object = "ParamWithShapeFamParameter")

show

signature(object = "ParamWithScaleAndShapeFamParameter")

Details for methods 'show', 'print'

Detailedness of output by methods show, print is controlled by the global option show.details to be set by distrModoptions.

As method show is used when inspecting an object by typing the object's name into the console, show comes without extra arguments and hence detailedness must be controlled by global options.

Method print may be called with a (partially matched) argument show.details, and then the global option is temporarily set to this value.

More specifically, when show.detail is matched to "minimal" only class and name as well as main and nuisance part of the parameter are shown. When show.detail is matched to "medium", and if you estimate non-trivial (i.e. not the identity) transformation of the parameter of the parametric family, you will in addition be shown the derivative matrix, if the transformation is given in form of this matrix, while, if the transformation is in function form, you will only be told this. Finally, when show.detail is matched to "maximal", and you have a non-trivial transformation in function form, you will also be shown the code to this function.

Author(s)

Matthias Kohl [email protected],
Peter Ruckdeschel [email protected]

See Also

Parameter-class

Examples

new("ParamFamParameter")

Generating function for Poisson families

Description

Generates an object of class "L2ParamFamily" which represents a Poisson family.

Usage

PoisFamily(lambda = 1, trafo)

Arguments

lambda

positive mean

trafo

function in param or matrix: transformation of the parameter

Details

The slots of the corresponding L2 differentiable parameteric family are filled.

Value

Object of class "L2ParamFamily"

Author(s)

Matthias Kohl [email protected]

References

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

L2ParamFamily-class, Pois-class

Examples

(P1 <- PoisFamily(lambda = 4.5))
plot(P1)
FisherInfo(P1)
checkL2deriv(P1)

Generating function for onesidedBias-class

Description

Generates an object of class "onesidedBias".

Usage

positiveBias(name = "positive Bias")

Arguments

name

name of the bias type

Value

Object of class "onesidedBias"

Author(s)

Peter Ruckdeschel [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Ruckdeschel, P. (2005) Optimally One-Sided Bounded Influence Curves. Mathematical Methods in Statistics 14(1), 105-131.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

onesidedBias-class

Examples

positiveBias()

## The function is currently defined as
function(){ new("onesidedBias", name = "positive Bias", sign = 1) }

Family of probability measures

Description

Class of families of probability measures.

Objects from the Class

A virtual Class: No objects may be created from it.

Slots

name

Object of class "character": name of the family.

distribution

Object of class "Distribution": member of the family.

distrSymm

Object of class "DistributionSymmetry": symmetry of distribution.

props

Object of class "character": properties of the family.

Methods

name

signature(object = "ProbFamily"): accessor function for slot name.

name<-

signature(object = "ProbFamily"): replacement function for slot name.

distribution

signature(object = "ProbFamily"): accessor function for slot distribution.

distrSymm

signature(object = "ProbFamily"): accessor function for slot distrSymm.

props

signature(object = "ProbFamily"): accessor function for slot props.

props<-

signature(object = "ProbFamily"): replacement function for slot props.

addProp<-

signature(object = "ProbFamily"): add a property to slot props.

r

signature(object = "ProbFamily"): wrapped accessor to slot r of slot "Distribution".

d

signature(object = "ProbFamily"): wrapped accessor to slot d of slot "Distribution".

p

signature(object = "ProbFamily"): wrapped accessor to slot p of slot "Distribution".

q

signature(object = "ProbFamily"): wrapped accessor to slot q of slot "Distribution".

q.l

signature(object = "ProbFamily"): wrapped accessor to slot q of slot "Distribution" – for compatibility with RStudio or Jupyter IRKernel / synonymous to q.

Author(s)

Matthias Kohl [email protected]

See Also

Distribution-class


Generating function for QFNorm-class

Description

Generates an object of class "QFNorm".

Usage

QFNorm(name = "norm based on quadratic form", 
       QuadForm = PosSemDefSymmMatrix(matrix(1)))

Arguments

name

slot name of the class

QuadForm

slot QuadForm of the class

Value

Object of class "QFNorm"

Author(s)

Peter Ruckdeschel [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

QFNorm-class

Examples

## IGNORE_RDIFF_BEGIN
QFNorm()

## The function is currently defined as
function(){ new("QFNorm") }
## IGNORE_RDIFF_END

Norm classes for norms based on quadratic forms

Description

Classes for norms based on quadratic forms

Objects from the Class

could be created by a call to new, but normally one would use the generating functions QFNorm, InfoNorm, and SelfNorm

Slots

name

Object of class "character".

fct

Object of class "function".

QuadForm

Object of class "PosSemDefSymmMatrix".

Extends

"QFNorm" extends class "NormType", directly, and "InfoNorm" and "SelfNorm" each extend class "QFNorm", directly (and do not have extra slots).

Methods

QuadForm

signature(object = "QFNorm"): accessor function for slot QuadForm.

QuadForm<-

signature(object = "QFNorm"): replacement function for slot QuadForm.

Author(s)

Peter Ruckdeschel [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Ruckdeschel, P. and Rieder, H. (2004) Optimal Influence Curves for General Loss Functions. Statistics & Decisions 22, 201-223.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

NormType-class


Methods for Function qqplot in Package ‘distrMod’

Description

We generalize function qqplot from package stats to be applicable to distribution and probability model objects, as well as to estimate objects. In this context, qqplot produces a QQ plot of data (argument x) against a (model) distribution. If the second argument is of class 'Estimate', qqplot looks at the estimate.call-slot and checks whether it can use an argument ParamFamily to conclude on the model distribution. Graphical parameters may be given as arguments to qqplot. In all title and label arguments, if withSubst is TRUE, the following patterns are substituted:

"%C"

class of argument x

"%A"

deparsed argument x

"%D"

time/date-string when the plot was generated

Usage

qqplot(x, y, ...)
## S4 method for signature 'ANY,UnivariateDistribution'
qqplot(x,y,
    n = length(x), withIdLine = TRUE,
    withConf = TRUE, withConf.pw  = withConf, withConf.sim = withConf,
    plot.it = TRUE, datax = FALSE, xlab = deparse(substitute(x)),
    ylab = deparse(substitute(y)),
    ..., width = 10, height = 5.5, withSweave = getdistrOption("withSweave"),
    mfColRow = TRUE, n.CI = n, with.lab = FALSE, lab.pts = NULL, which.lbs = NULL,
    which.Order = NULL, which.nonlbs = NULL, attr.pre = FALSE, order.traf = NULL,
    col.IdL = "red", lty.IdL = 2, lwd.IdL = 2, alpha.CI = .95,
    exact.pCI = (n<100), exact.sCI = (n<100), nosym.pCI = FALSE,
    col.pCI = "orange", lty.pCI = 3, lwd.pCI = 2, pch.pCI = par("pch"),
    cex.pCI = par("cex"),
    col.sCI = "tomato2", lty.sCI = 4, lwd.sCI = 2, pch.sCI = par("pch"),
    cex.sCI = par("cex"), added.points.CI = TRUE,
    cex.pch = par("cex"), col.pch = par("col"),
    cex.pts = 1, col.pts = par("col"), pch.pts = 19,
    cex.npts = 1, col.npts = grey(.5), pch.npts = 20,
    cex.lbs = par("cex"), col.lbs = par("col"), adj.lbs = par("adj"),
    alpha.trsp = NA, jit.fac = 0, jit.tol = .Machine$double.eps,
    check.NotInSupport = TRUE, col.NotInSupport = "red",
    with.legend = TRUE, legend.bg = "white",
    legend.pos = "topleft", legend.cex = 0.8, 
    legend.pref = "", legend.postf = "",  legend.alpha = alpha.CI,
    debug = FALSE, withSubst = TRUE)
## S4 method for signature 'ANY,ProbFamily'
qqplot(x, y,
   n = length(x), withIdLine = TRUE, withConf = TRUE,
   withConf.pw  = withConf,  withConf.sim = withConf,
    plot.it = TRUE, xlab = deparse(substitute(x)),
    ylab = deparse(substitute(y)), ...)
## S4 method for signature 'ANY,Estimate'
qqplot(x, y,
   n = length(x), withIdLine = TRUE, withConf = TRUE,
   withConf.pw  = withConf,  withConf.sim = withConf,
    plot.it = TRUE, xlab = deparse(substitute(x)),
    ylab = deparse(substitute(y)), ...)

Arguments

x

data to be checked for compatibility with distribution/model y.

y

object of class "UnivariateDistribution" or of class "ProbFamily".

n

numeric; assumed sample size (by default length of x).

withIdLine

logical; shall line y = x be plotted in?

withConf

logical; shall confidence lines be plotted?

withConf.pw

logical; shall pointwise confidence lines be plotted?

withConf.sim

logical; shall simultaneous confidence lines be plotted?

plot.it

logical; shall be plotted at all (inherited from qqplot)?

datax

logical; shall data be plotted on x-axis?

xlab

x-label

ylab

y-label

...

further parameters for method qqplot with signature ANY,UnivariateDistribution or with function plot

width

width (in inches) of the graphics device opened

height

height (in inches) of the graphics device opened

withSweave

logical: if TRUE (for working with Sweave) no extra device is opened and height/width are not set

mfColRow

shall default partition in panels be used — defaults to TRUE

n.CI

numeric; number of points to be used for confidence interval

with.lab

logical; shall observation labels be plotted in?

lab.pts

character or NULL; observation labels to be used

attr.pre

logical; do graphical attributes for plotted data refer to indices prior (TRUE) or posterior to selection via arguments which.lbs, which.Order, which.nonlbs (FALSE)?

which.lbs

integer or NULL; which observations shall be labelled

which.Order

integer or NULL; which of the ordered (remaining) observations shall be labelled

which.nonlbs

indices of the observations which should be plotted but not labelled; either an integer vector with the indices of the observations to be plotted into graph or NULL — then all non-labelled observations are plotted.

order.traf

function or NULL; an optional trafo by which the observations are ordered (as order(trafo(obs)).

col.IdL

color for the identity line

lty.IdL

line type for the identity line

lwd.IdL

line width for the identity line

alpha.CI

confidence level

exact.pCI

logical; shall pointwise CIs be determined with exact Binomial distribution?

exact.sCI

logical; shall simultaneous CIs be determined with exact Kolmogorov distribution?

nosym.pCI

logical; shall we use (shortest) asymmetric CIs?

col.pCI

color for the pointwise CI

lty.pCI

line type for the pointwise CI

lwd.pCI

line width for the pointwise CI

pch.pCI

symbol for points (for discrete mass points) in pointwise CI

cex.pCI

magnification factor for points (for discrete mass points) in pointwise CI

col.sCI

color for the simultaneous CI

lty.sCI

line type for the simultaneous CI

lwd.sCI

line width for the simultaneous CI

pch.sCI

symbol for points (for discrete mass points) in simultaneous CI

cex.sCI

magnification factor for points (for discrete mass points) in simultaneous CI

added.points.CI

logical; should CIs be plotted through additional points (and not only through data points)?

cex.pch

magnification factor for the plotted symbols (for backward compatibility); it is ignored once col.pts is specified.

col.pch

color for the plotted symbols (for backward compatibility); it is ignored once col.pts is specified.

cex.pts

size of the points of the second argument plotted, can be a vector; if argument attr.pre is TRUE, it is recycled to the length of all observations and determines the sizes of all plotted symbols, i.e., the selection is done within this argument; in this case argument col.npts is ignored. If attr.pre is FALSE, cex.pts is recycled to the number of the observations selected for labelling and refers to the index ordering after the selection. Then argument cex.npts deteremines the sizes of the shown but non-labelled observations as given in argument which.nonlbs.

col.pts

color of the points of the second argument plotted, can be a vector as in cex.pts (with col.npts as counterpart).

pch.pts

symbol of the points of the second argument plotted, can be a vector as in cex.pts (with pch.npts as counterpart).

col.npts

color of the non-labelled points of the data argument plotted; (may be a vector).

pch.npts

symbol of the non-labelled points of the data argument plotted (may be a vector).

cex.npts

size of the non-labelled points of the data argument plotted (may be a vector).

cex.lbs

magnification factor for the plotted observation labels

col.lbs

color for the plotted observation labels

adj.lbs

adj parameter for the plotted observation labels

alpha.trsp

alpha transparency to be added ex post to colors col.pch and col.lbs; if one-dim and NA all colors are left unchanged. Otherwise, with usual recycling rules alpha.trsp gets shorted/prolongated to length the data-symbols to be plotted. Coordinates of this vector alpha.trsp with NA are left unchanged, while for the remaining ones, the alpha channel in rgb space is set to the respective coordinate value of alpha.trsp. The non-NA entries must be integers in [0,255] (0 invisible, 255 opaque).

jit.fac

jittering factor used for discrete distributions.

jit.tol

threshold for jittering: if distance between points is smaller than jit.tol, points are considered replicates.

check.NotInSupport

logical; shall we check if all x-quantiles lie in support(y)?

col.NotInSupport

logical; if preceding check TRUE color of x-quantiles if not in support(y)

with.legend

logical; shall a legend be plotted?

legend.bg

background color for the legend

legend.pos

position for the legend

legend.cex

magnification factor for the legend

legend.pref

character to be prepended to legend text

legend.postf

character to be appended to legend text

legend.alpha

nominal coverage probability

debug

logical; if TRUE additional output to debug confidence bounds.

withSubst

logical; if TRUE (default) pattern substitution for titles and axis lables is used; otherwise no substitution is used.

Details

qqplot

signature(x = "ANY", y = "UnivariateDistribution"): produces a QQ plot of a dataset x against the theoretical quantiles of distribution y.

qqplot

signature(x = "ANY", y = "ProbFamily"): produces a QQ plot of a dataset x against the theoretical quantiles of the model distribution of model y. Passed through the ... argument, all arguments valid for signature(x = "ANY", y = "UnivariateDistribution") are also valid for this signature.

qqplot

signature(x = "ANY", y = "Estimate"): produces a QQ plot of a dataset x against the theoretical quantiles of the model distribution of the model that can be reconstructed from the estimator y; more specifically, it tries to get hand at the argument 'ParamFamily' of the esimator's call; if this is available, internally this model is shifted to the estimated parameter by a call to modifyModel, and then this shifted model is used in a call to the (x = "ANY", y = "UnivariateDistribution")-method. Passed through the ... argument, all arguments valid for signature(x = "ANY", y = "UnivariateDistribution") are also valid for this signature.

Value

As for function qqplot from package stats: a list with components

x

The x coordinates of the points that were/would be plotted

y

The corresponding quantiles of the second distribution, including NAs.

crit

A matrix with the lower and upper confidence bounds (computed by qqbounds).

err

logical vector of length 2.

(elements crit and err are taken from the return value(s) of qqbounds).

Author(s)

Peter Ruckdeschel [email protected]

References

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole.

See Also

qqplot from package stats – the standard QQ plot function, qqplot from package distr for comparisons of distributions, and qqbounds, used by qqplot to produce confidence intervals.

Examples

set.seed(123)
x <- rnorm(40,mean=15,sd=30)
qqplot(x, Chisq(df=15))
NF <- NormLocationScaleFamily(mean=15, sd=30)
qqplot(x, NF, with.lab=TRUE, which.Order=1:5, cex.lbs=1.3)
mlE <- MLEstimator(x, NF)
qqplot(x, mlE)

Methods for Function returnlevelplot in Package ‘distrMod’

Description

We generalize the return level plot (which is one of the diagnostical plots provided package ismev, e.g., in function gev.diag), see also Coles' book below, to be applicable to distribution and probability model objects. In this context, returnlevelplot produces a rescaled QQ plot of data (argument x) against a (model) distribution. Graphical parameters may be given as arguments to returnlevelplot. In all title and label arguments, if withSubst is TRUE, the following patterns are substituted:

"%C"

class of argument x

"%A"

deparsed argument x

"%D"

time/date-string when the plot was generated

Usage

returnlevelplot(x, y, ...)
## S4 method for signature 'ANY,UnivariateDistribution'
returnlevelplot(x,y,
    n = length(x), withIdLine = TRUE,
    withConf = TRUE, withConf.pw  = withConf, withConf.sim = withConf,
    plot.it = TRUE, datax = FALSE, MaxOrPOT = c("Max","POT"), npy = 365,
    threshold = if(is(y,"GPareto")) NA else 0,    
    xlab = deparse(substitute(x)),
    ylab = deparse(substitute(y)),
    main = "",
    ..., width = 10, height = 5.5, withSweave = getdistrOption("withSweave"),
    mfColRow = TRUE, n.CI = n, with.lab = FALSE, lab.pts = NULL, which.lbs = NULL,
    which.Order = NULL, which.nonlbs = NULL, attr.pre = FALSE, order.traf = NULL,
    col.IdL = "red", lty.IdL = 2, lwd.IdL = 2, alpha.CI = .95,
    exact.pCI = (n<100), exact.sCI = (n<100), nosym.pCI = FALSE,
    col.pCI = "orange", lty.pCI = 3, lwd.pCI = 2, pch.pCI = par("pch"),
    cex.pCI = par("cex"),
    col.sCI = "tomato2", lty.sCI = 4, lwd.sCI = 2, pch.sCI = par("pch"),
    cex.sCI = par("cex"), added.points.CI = TRUE,
    cex.pch = par("cex"), col.pch = par("col"),
    cex.pts = 1, col.pts = par("col"), pch.pts = 19,
    cex.npts = 1, col.npts = grey(.5), pch.npts = 20,
    cex.lbs = par("cex"), col.lbs = par("col"), adj.lbs = par("adj"),
    alpha.trsp = NA, jit.fac = 0,  jit.tol = .Machine$double.eps,
    check.NotInSupport = TRUE, col.NotInSupport = "red",
    with.legend = TRUE, legend.bg = "white",
    legend.pos = "topleft", legend.cex = 0.8,
    legend.pref = "", legend.postf = "",  legend.alpha = alpha.CI,
    debug = FALSE, withSubst = TRUE)
## S4 method for signature 'ANY,ProbFamily'
returnlevelplot(x, y,
   n = length(x), withIdLine = TRUE, withConf = TRUE,
   withConf.pw  = withConf,  withConf.sim = withConf,
    plot.it = TRUE, xlab = deparse(substitute(x)),
    ylab = deparse(substitute(y)), ...)
## S4 method for signature 'ANY,Estimate'
returnlevelplot(x, y,
   n = length(x), withIdLine = TRUE, withConf = TRUE,
   withConf.pw  = withConf,  withConf.sim = withConf,
    plot.it = TRUE, xlab = deparse(substitute(x)),
    ylab = deparse(substitute(y)), ...)

Arguments

x

data to be checked for compatibility with distribution/model y.

y

object of class "UnivariateDistribution" or of class "ProbFamily".

n

numeric; assumed sample size (by default length of x).

withIdLine

logical; shall line y = x be plotted in?

withConf

logical; shall confidence lines be plotted?

withConf.pw

logical; shall pointwise confidence lines be plotted?

withConf.sim

logical; shall simultaneous confidence lines be plotted?

plot.it

logical; shall be plotted at all (inherited from returnlevelplot)?

datax

logical; shall data be plotted on x-axis?

MaxOrPOT

a character string specifying whether it is used for block maxima ("Max") or for points over threshold ("POT"); must be one of "Max" (default) or "POT". You can specify just the initial letter.

npy

number of observations per year/block.

threshold

numerical; in case of MaxOrPot=="POT", this captures the (removed) threshold. If it is NA, it is reconstructed from the distribution y.

main

Main title

xlab

x-label

ylab

y-label

...

further parameters for method returnlevelplot with signature ANY,UnivariateDistribution or with function plot

width

width (in inches) of the graphics device opened

height

height (in inches) of the graphics device opened

withSweave

logical: if TRUE (for working with Sweave) no extra device is opened and height/width are not set

mfColRow

shall default partition in panels be used — defaults to TRUE

n.CI

numeric; number of points to be used for confidence interval

with.lab

logical; shall observation labels be plotted in?

lab.pts

character or NULL; observation labels to be used

attr.pre

logical; do graphical attributes for plotted data refer to indices prior (TRUE) or posterior to selection via arguments which.lbs, which.Order, which.nonlbs (FALSE)?

which.lbs

integer or NULL; which observations shall be labelled

which.nonlbs

indices of the observations which should be plotted but not labelled; either an integer vector with the indices of the observations to be plotted into graph or NULL — then all non-labelled observations are plotted.

which.Order

integer or NULL; which of the ordered (remaining) observations shall be labelled

order.traf

function or NULL; an optional trafo by which the observations are ordered (as order(trafo(obs)).

col.IdL

color for the identity line

lty.IdL

line type for the identity line

lwd.IdL

line width for the identity line

alpha.CI

confidence level

exact.pCI

logical; shall pointwise CIs be determined with exact Binomial distribution?

exact.sCI

logical; shall simultaneous CIs be determined with exact Kolmogorov distribution?

nosym.pCI

logical; shall we use (shortest) asymmetric CIs?

col.pCI

color for the pointwise CI

lty.pCI

line type for the pointwise CI

lwd.pCI

line width for the pointwise CI

pch.pCI

symbol for points (for discrete mass points) in pointwise CI

cex.pCI

magnification factor for points (for discrete mass points) in pointwise CI

col.sCI

color for the simultaneous CI

lty.sCI

line type for the simultaneous CI

lwd.sCI

line width for the simultaneous CI

pch.sCI

symbol for points (for discrete mass points) in simultaneous CI

cex.sCI

magnification factor for points (for discrete mass points) in simultaneous CI

added.points.CI

logical; should CIs be plotted through additional points (and not only through data points)?

cex.pch

magnification factor for the plotted symbols (for backward compatibility); it is ignored once col.pts is specified.

col.pch

color for the plotted symbols (for backward compatibility); it is ignored once col.pts is specified.

cex.pts

size of the points of the second argument plotted, can be a vector; if argument attr.pre is TRUE, it is recycled to the length of all observations and determines the sizes of all plotted symbols, i.e., the selection is done within this argument; in this case argument col.npts is ignored. If attr.pre is FALSE, cex.pts is recycled to the number of the observations selected for labelling and refers to the index ordering after the selection. Then argument cex.npts deteremines the sizes of the shown but non-labelled observations as given in argument which.nonlbs.

col.pts

color of the points of the second argument plotted, can be a vector as in cex.pts (with col.npts as counterpart).

pch.pts

symbol of the points of the second argument plotted, can be a vector as in cex.pts (with pch.npts as counterpart).

col.npts

color of the non-labelled points of the data argument plotted; (may be a vector).

pch.npts

symbol of the non-labelled points of the data argument plotted (may be a vector).

cex.npts

size of the non-labelled points of the data argument plotted (may be a vector).

cex.lbs

magnification factor for the plotted observation labels

col.lbs

color for the plotted observation labels

adj.lbs

adj parameter for the plotted observation labels

alpha.trsp

alpha transparency to be added ex post to colors col.pch and col.lbs; if one-dim and NA all colors are left unchanged. Otherwise, with usual recycling rules alpha.trsp gets shorted/prolongated to length the data-symbols to be plotted. Coordinates of this vector alpha.trsp with NA are left unchanged, while for the remaining ones, the alpha channel in rgb space is set to the respective coordinate value of alpha.trsp. The non-NA entries must be integers in [0,255] (0 invisible, 255 opaque).

jit.fac

jittering factor used for discrete distributions.

jit.tol

threshold for jittering: if distance between points is smaller than jit.tol, points are considered replicates.

check.NotInSupport

logical; shall we check if all x-quantiles lie in support(y)?

col.NotInSupport

logical; if preceding check TRUE color of x-quantiles if not in support(y)

with.legend

logical; shall a legend be plotted?

legend.bg

background color for the legend

legend.pos

position for the legend

legend.cex

magnification factor for the legend

legend.pref

character to be prepended to legend text

legend.postf

character to be appended to legend text

legend.alpha

nominal coverage probability

debug

logical; if TRUE additional output to debug confidence bounds.

withSubst

logical; if TRUE (default) pattern substitution for titles and axis lables is used; otherwise no substitution is used.

Details

returnlevelplot

signature(x = "ANY", y = "UnivariateDistribution"): produces a return level plot of a dataset x against the theoretical quantiles of distribution y.

returnlevelplot

signature(x = "ANY", y = "ProbFamily"): produces a return level plot of a dataset x against the theoretical quantiles of the model distribution of model y. Passed through the ... argument, all arguments valid for signature(x = "ANY", y = "UnivariateDistribution") are also valid for this signature.

returnlevelplot

signature(x = "ANY", y = "Estimate"): produces a return level plot of a dataset x against the theoretical quantiles of the model distribution of the model that can be reconstructed from the estimator y; more specifically, it tries to get hand at the argument 'ParamFamily' of the esimator's call; if this is available, internally this model is shifted to the estimated parameter by a call to modifyModel, and then this shifted model is used in a call to the (x = "ANY", y = "UnivariateDistribution")-method. Passed through the ... argument, all arguments valid for signature(x = "ANY", y = "UnivariateDistribution") are also valid for this signature.

Value

As for function returnlevelplot from package stats: a list with components

x

The x coordinates of the points that were/would be plotted

y

The corresponding quantiles of the second distribution, including NAs.

crit

A matrix with the lower and upper confidence bounds (computed by qqbounds).

err

logical vector of length 2.

(elements crit and err are taken from the return value(s) of qqbounds).

Note

The confidence bands given in our version of the return level plot differ from the ones given in package ismev. We use non-parametric bands, hence also allow for non-parametric deviances from the model, whereas in in package ismev they are based on profiling, hence only check for variability within the parametric class.

Author(s)

Peter Ruckdeschel [email protected]

References

ismev: An Introduction to Statistical Modeling of Extreme Values. R package version 1.39. https://CRAN.R-project.org/package=ismev; original S functions written by Janet E. Heffernan with R port and R documentation provided by Alec G. Stephenson. (2012).

Coles, S. (2001). An introduction to statistical modeling of extreme values. London: Springer.

See Also

qqplot from package stats – the standard QQ plot function, qqplot from package distr for comparisons of distributions, qqplot from this package and qqbounds, used by returnlevelplot to produce confidence intervals.

Examples

set.seed(20190331)
returnlevelplot(r(Norm(15,sqrt(30)))(40), Chisq(df=15))
### more could be seen after installing RobExtremes and ismev
#

## IGNORE_RDIFF_BEGIN
 ## at R CMD check --as-cran, it does not find package cluster
           ## when trying to attach package rrcov
           ## so remove this from testing
if(require(RobExtremes) && require(ismev)){

 data(portpirie)
 gevfit <- gev.fit(portpirie[,2]) ## taken from example from ismev::gev.fit
 GEVF <- GEVFamily(scale=gevfit$mle[2],shape=gevfit$mle[3],loc=gevfit$mle[1])
 erg <- returnlevelplot(portpirie[,2], GEVF)
 print(names(erg))
 print(names(erg$plotArgs))
 print(names(erg$IdLineArgs))
 returnlevelplot(portpirie[,2], GEVF, datax=TRUE)

 data(rain)
 gpdfit <- gpd.fit(rain,10) ## taken from example from ismev::gpd.fit
 GPDF <- GParetoFamily(scale=gpdfit$mle[1],shape=gpdfit$mle[2],loc=10)
 returnlevelplot(rain, GPDF, MaxOrPOT="POT", xlim=c(1e-1,1e3))
}

## IGNORE_RDIFF_END

Risk

Description

Class of risks; e.g., estimator risks.

Objects from the Class

A virtual Class: No objects may be created from it.

Slots

type

Object of class "character": type of risk.

Methods

type

signature(object = "RiskType"): accessor function for slot type.

show

signature(object = "RiskType")

Author(s)

Matthias Kohl [email protected]


Generating function for SelfNorm-class

Description

Generates an object of class "SelfNorm" — used for self-standardized influence curves.

Usage

SelfNorm()

Value

Object of class "SelfNorm"

Author(s)

Matthias Kohl [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

SelfNorm-class

Examples

## IGNORE_RDIFF_BEGIN
SelfNorm()

## The function is currently defined as
function(){ new("SelfNorm") }
## IGNORE_RDIFF_END

Generating function for symmetricBias-class

Description

Generates an object of class "symmetricBias".

Usage

symmetricBias(name = "symmetric Bias")

Arguments

name

name of the bias type

Value

Object of class "symmetricBias"

Author(s)

Peter Ruckdeschel [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Ruckdeschel, P. (2005) Optimally One-Sided Bounded Influence Curves. Mathematical Methods in Statistics 14(1), 105-131.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

symmetricBias-class

Examples

symmetricBias()

## The function is currently defined as
function(){ new("symmetricBias", name = "symmetric Bias") }

symmetric Bias Type

Description

Class of symmetric bias types.

Objects from the Class

Objects can be created by calls of the form new("symmetricBias", ...). More frequently they are created via the generating function symmetricBias.

Slots

name

Object of class "character".

Methods

No methods defined with class "symmetricBias" in the signature.

Extends

Class "BiasType", directly.

Author(s)

Peter Ruckdeschel [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Ruckdeschel, P. (2005) Optimally One-Sided Bounded Influence Curves. Mathematical Methods in Statistics 14(1), 105-131.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

BiasType-class

Examples

symmetricBias()
## The function is currently defined as
function(){ new("symmetricBias", name = "symmetric Bias") }

Methods for function trafo in Package ‘distrMod’

Description

Methods for function trafo in package distrMod; there are accessor (trafo) and replacement (trafo<-) versions.

Usage

trafo(object, param, ...)
## S4 method for signature 'Estimate,missing'
trafo(object,param)
## S4 method for signature 'ParamFamParameter,missing'
trafo(object,param)
## S4 method for signature 'ParamWithScaleAndShapeFamParameter,missing'
trafo(object,param)
## S4 method for signature 'ParamFamily,missing'
trafo(object,param)
## S4 method for signature 'ParamFamily,ParamFamParameter'
trafo(object,param)
## S4 method for signature 'Estimate,ParamFamParameter'
trafo(object,param)
trafo.fct(object)
trafo(object) <- value

Arguments

object

an object of either class Estimate, ParamFamParameter, ParamFamily

param

an object of class ParamFamParameter; the parameter value at which to evaluate the transformation

value

a matrix or a function; if it is a matrix, dimensions must be consistent to the parametric setting; if it is function, it should take one argument param of class ParamFamParameter and return a list of length two with named components fval (the function value, see below) and mat (a matrix — with the same dimensions consistency conditions as above).

...

additional argument(s) for methods; not used so far.

Details

trafo is a slot of class ParamFamParameter, which in turn is a slot of class ParamFamily. It also sort of arises in class Estimate, i.e., all slots can be identified by the information contained in an instance thereof.

As usual, trafo also is the accessor and replacement method for this slot. Its corresponding return value depends on the signature for which the accessor / replacement method is used. More specifically, for trafo, we have methods for the following signatures:

signature Estimate,missing:

returns a list of length two with components fct and mat (see below)

signature Estimate,ParamFamParameter:

returns a list of length two with components fct and mat (see below)

signature ParamFamParameter,missing:

returns a matrix (see below)

signature ParamFamily,missing:

returns a matrix (see below)

signature ParamFamily,ParamFamParameter:

returns a list of length two with components fct and mat (see below)

trafo realizes partial influence curves; i.e.; we are only interested in some possibly lower dimensional smooth (not necessarily linear or even coordinate-wise) aspect/transformation τ\tau of the parameter θ\theta.

For the this function τ()\tau(), we provide an accessor trafo.fct for signature ParamFamily-method returning this function.

To be coherent with the corresponding nuisance implementation, we make the following convention:

The full parameter θ\theta is split up coordinate-wise in a main parameter θ\theta' and a nuisance parameter θ\theta'' (which is unknown, too, hence has to be estimated, but only is of secondary interest) and a fixed, known part θ\theta'''.

Without loss of generality, we restrict ourselves to the case that transformation τ\tau only acts on the main parameter θ\theta' — if we want to transform the whole parameter, we only have to assume that both nuisance parameter θ\theta'' and fixed, known part of the parameter θ\theta''' have length 0.

To the implementation:

Slot trafo can either contain a (constant) matrix DθD_\theta or a function

τ ⁣:ΘΘ~,θτ(θ)\tau\colon \Theta' \to \tilde \Theta,\qquad \theta \mapsto \tau(\theta)

mapping main parameter θ\theta' to some range Θ~\tilde \Theta.

If slot value trafo is a function, besides τ(θ)\tau(\theta), it will also return the corresponding derivative matrix θτ(θ)\frac{\partial}{\partial \theta}\tau(\theta). More specifically, the return value of this function theta is a list with entries fval, the function value τ(θ)\tau(\theta), and mat, the derivative matrix.

In case trafo is a matrix DD, we interpret it as such a derivative matrix θτ(θ)\frac{\partial}{\partial \theta}\tau(\theta), and, correspondingly, τ(θ)\tau(\theta) as the linear mapping τ(θ)=Dθ\tau(\theta)=D\,\theta.

According to the signature, method trafo will return different return value types. For signature

Estimate,missing:

it will return a list with entries fct, the function τ\tau, and mat, the matrix θτ(θ)\frac{\partial}{\partial \theta}\tau(\theta). function τ\tau will then return the list list(fval, mat) mentioned above.

Estimate,ParamFamParameter:

as signature Estimate,missing.

ParamFamParameter,missing:

it will just return the corresponding matrix.

ParamFamily,missing:

is just wrapper to signature ParamFamParameter,missing.

ParamFamily,ParamFamParameter:

as signature Estimate,missing.

Examples

## Gaussian location and scale
NS <- NormLocationScaleFamily(mean=2, sd=3)
## generate data out of this situation
x <- r(distribution(NS))(30)

## want to estimate mu/sigma, sigma^2
## -> new trafo slot:
trafo(NS) <- function(param){
  mu <- param["mean"]
  sd <- param["sd"]
  fval <- c(mu/sd, sd^2)
  nfval <- c("mu/sig", "sig^2")
  names(fval) <- nfval
  mat <- matrix(c(1/sd,0,-mu/sd^2,2*sd),2,2)
  dimnames(mat) <- list(nfval,c("mean","sd"))
  return(list(fval=fval, mat=mat))
}

## Maximum likelihood estimator
(res <- MLEstimator(x = x, ParamFamily = NS))
## confidence interval
 confint(res)

Function trafoEst in Package ‘distrMod’

Description

trafoEst takes a τ\tau like function (compare trafo-methods) and transforms an existing estimator by means of this transformation.

Usage

trafoEst(fct, estimator)

Arguments

fct

a τ\tau like function, i.e., a function in the main part θ\theta of the parameter returning a list list(fval, mat) where fval is the function value τ(θ)\tau(\theta) of the transformation, and mat, its derivative matrix at θ\theta.

estimator

an object of class Estimator.

Details

The disadvantage of this proceeding is that the transformation is not accounted for in determining the estimate (e.g. in a corresponding optimality); it simply transforms an existing estimator, without reapplying it to data. This becomes important in optimally robust estimation.

Value

exactly the argument estimator, but with modified slots estimate, asvar, and trafo.

Examples

## Gaussian location and scale
NS <- NormLocationScaleFamily(mean=2, sd=3)
## generate data out of this situation
x <- r(distribution(NS))(30)

## want to estimate mu/sigma, sigma^2
## -> without new trafo slot:
mtrafo <- function(param){
  mu <- param["mean"]
  sd <- param["sd"]
  fval <- c(mu/sd, sd^2)
  nfval <- c("mu/sig", "sig^2")
  names(fval) <- nfval
  mat <- matrix(c(1/sd,0,-mu/sd^2,2*sd),2,2)
  dimnames(mat) <- list(nfval,c("mean","sd"))
  return(list(fval=fval, mat=mat))
}

## Maximum likelihood estimator in the original problem
res0 <- MLEstimator(x = x, ParamFamily = NS)
## transformation
res <- trafoEst(mtrafo, res0)
## confidence interval
 confint(res)

Generating function for trAsCov-class

Description

Generates an object of class "trAsCov".

Usage

trAsCov()

Value

Object of class "trAsCov"

Author(s)

Matthias Kohl [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

trAsCov-class

Examples

trAsCov()

## The function is currently defined as
function(){ new("trAsCov") }

Trace of asymptotic covariance

Description

Class of trace of asymptotic covariance.

Objects from the Class

Objects can be created by calls of the form new("trAsCov", ...). More frequently they are created via the generating function trAsCov.

Slots

type

Object of class "character": “trace of asymptotic covariance”.

Extends

Class "asRisk", directly.
Class "RiskType", by class "asRisk".

Author(s)

Matthias Kohl [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

asRisk-class, trAsCov

Examples

new("trAsCov")

Generating function for trFiCov-class

Description

Generates an object of class "trFiCov".

Usage

trFiCov()

Value

Object of class "trFiCov"

Author(s)

Matthias Kohl [email protected]

References

Ruckdeschel, P. and Kohl, M. (2005) How to approximate the finite sample risk of M-estimators.

See Also

trFiCov-class

Examples

trFiCov()

## The function is currently defined as
function(){ new("trFiCov") }

Trace of finite-sample covariance

Description

Class of trace of finite-sample covariance.

Objects from the Class

Objects can be created by calls of the form new("trFiCov", ...). More frequently they are created via the generating function trFiCov.

Slots

type

Object of class "character": “trace of finite-sample covariance”.

Extends

Class "fiRisk", directly.
Class "RiskType", by class "fiRisk".

Author(s)

Matthias Kohl [email protected]

References

Ruckdeschel, P. and Kohl, M. (2005) How to approximate the finite sample risk of M-estimators.

See Also

fiRisk-class, trFiCov

Examples

new("trFiCov")

Methods for function validParameter in Package ‘distrMod’

Description

Methods for function validParameter in package distrMod to check whether a new parameter (e.g. "proposed" by an optimization) is valid.

Usage

validParameter(object, ...)
## S4 method for signature 'ParamFamily'
validParameter(object, param)
## S4 method for signature 'L2ScaleUnion'
validParameter(object, param, tol=.Machine$double.eps)
## S4 method for signature 'L2ScaleFamily'
validParameter(object, param, tol=.Machine$double.eps)
## S4 method for signature 'L2LocationFamily'
validParameter(object, param)
## S4 method for signature 'L2LocationScaleFamily'
validParameter(object, param, tol=.Machine$double.eps)
## S4 method for signature 'BinomFamily'
validParameter(object, param, tol=.Machine$double.eps)
## S4 method for signature 'PoisFamily'
validParameter(object, param, tol=.Machine$double.eps)
## S4 method for signature 'L2ScaleShapeUnion'
validParameter(object, param, tol=.Machine$double.eps)

Arguments

object

an object of class ParamFamily

param

either a numeric vector or an object of class ParamFamParameter

tol

accuracy upto which the conditions have to be fulfilled

...

additional argument(s) for methods.

Details

method for signature

ParamFamily

checks if all parameters are finite by is.finite if their length is between 1 and the joint length of main and nuisance parameter of object, and finally, if a call to modifyParam(object) with argument param would throw an error.

L2ScaleUnion

checks if the parameter is finite by is.finite, and if it is strictly larger than 0 (upto argument tol).

L2ScaleFamily

checks if the parameter length is 1, and otherwise uses L2ScaleUnion-method.

L2LocationFamily

checks if the parameter is finite by is.finite, if its length is 1

L2LocationScaleFamily

checks if the parameter length is 1 or 2 (e.g. if one features as nuisance parameter), and also uses L2ScaleUnion-method.

BinomFamily

checks if the parameter is finite by is.finite, if its length is 1, and if it is strictly larger than 0 and strictly smaller than 1 (upto argument tol)

PoisFamily

checks if the parameter is finite by is.finite, if its length is 1, and if it is strictly larger than 0 (upto argument tol)

L2ScaleShapeUnion

uses L2ScaleUnion-method, checks if parameter length is 1 or 2 (e.g. if one features as nuisance parameter), and if shape is strictly larger than 0 (upto argument tol)

Value

logical of length 1 — valid or not

Examples

NS <- NormLocationScaleFamily()
 validParameter(NS, c(scale=0.1, loc=2))
 validParameter(NS, c(scale=-0.1, loc=2))
 validParameter(NS, c(scale=0, loc=2))
 validParameter(NS, c(mean=2, sd=2))