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 |
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.
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 |
[*]: 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"
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
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",
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 are available — see demo(package="distrMod")
.
Example scripts are available — see folder ‘scripts’ in the package folder to package distrMod in your library.
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.
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()
Peter Ruckdeschel [email protected],
Matthias Kohl [email protected]
Maintainer: Peter Ruckdeschel [email protected]
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")
.checkEstClassForParamFamily-methods
.checkEstClassForParamFamily(PFam, estimator) ## S4 method for signature 'ANY,ANY' .checkEstClassForParamFamily(PFam, estimator)
.checkEstClassForParamFamily(PFam, estimator) ## S4 method for signature 'ANY,ANY' .checkEstClassForParamFamily(PFam, estimator)
PFam |
a parametric family. |
estimator |
an estimator. |
The respective methods can be used to cast an estimator to a model-specific subclass with particular methods.
The (default) ANY,ANY
-method returns the estimator unchanged.
Peter Ruckdeschel [email protected]
Adds alpha transparency to a given color.
addAlphTrsp2col(col, alpha=255)
addAlphTrsp2col(col, alpha=255)
col |
any valid color |
alpha |
tranparancy; an integer value in [0,255] |
a color in rgb coordinates
Peter Ruckdeschel [email protected]
## 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)
## 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)
Generates an object of class "asBias"
.
asBias(biastype = symmetricBias(), normtype = NormType())
asBias(biastype = symmetricBias(), normtype = NormType())
biastype |
a bias type of class |
normtype |
a norm type of class |
Object of class "asBias"
Matthias Kohl [email protected]
Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.
asBias() ## The function is currently defined as function(biastype = symmetricBias(), normtype = NormType()){ new("asBias",biastype = biastype, normtype = normtype) }
asBias() ## The function is currently defined as function(biastype = symmetricBias(), normtype = NormType()){ new("asBias",biastype = biastype, normtype = normtype) }
Class of standardized asymptotic bias; i.e.,
the neighborhood radius is omitted respectively, set to .
Objects can be created by calls of the form new("asBias", ...)
.
More frequently they are created via the generating function
asBias
.
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
Class "asRiskwithBias"
, directly.
Class "asRisk"
, by class "asRiskwithBias"
Class "RiskType"
, by class "asRisk"
.
Matthias Kohl [email protected]
Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.
new("asBias")
new("asBias")
Generates an object of class "asCov"
.
asCov()
asCov()
Object of class "asCov"
Matthias Kohl [email protected]
Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.
asCov() ## The function is currently defined as function(){ new("asCov") }
asCov() ## The function is currently defined as function(){ new("asCov") }
Class of asymptotic covariance.
Objects can be created by calls of the form new("asCov", ...)
.
More frequently they are created via the generating function
asCov
.
type
Object of class "character"
:
“asymptotic covariance”.
Class "asRisk"
, directly.
Class "RiskType"
, by class "asRisk"
.
No methods defined with class "asCov" in the signature.
Matthias Kohl [email protected]
Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.
new("asCov")
new("asCov")
Class of special convex asymptotic risks.
A virtual Class: No objects may be created from it.
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
Class "asRisk"
, directly.
Class "RiskType"
, by class "asRisk"
.
No methods defined with class "asGRisk" in the signature.
Matthias Kohl [email protected]
Ruckdeschel, P. and Rieder, H. (2004) Optimal Influence Curves for General Loss Functions. Statistics & Decisions 22, 201-223.
Generates an object of class "asHampel"
.
asHampel(bound = Inf, biastype = symmetricBias(), normtype = NormType())
asHampel(bound = Inf, biastype = symmetricBias(), normtype = NormType())
bound |
positive real: bias bound |
biastype |
a bias type of class |
normtype |
a norm type of class |
Object of class asHampel
Matthias Kohl [email protected]
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.
asHampel() ## The function is currently defined as function(bound = Inf, biastype = symmetricBias(), normtype = NormType()){ new("asHampel", bound = bound, biastype = biastype, normtype = normtype) }
asHampel() ## The function is currently defined as function(bound = Inf, biastype = symmetricBias(), normtype = NormType()){ new("asHampel", bound = bound, biastype = biastype, normtype = normtype) }
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 can be created by calls of the form new("asHampel", ...)
.
More frequently they are created via the generating function
asHampel
.
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
Class "asRiskwithBias"
, directly.
Class "asRisk"
, by class "asRiskwithBias"
.
Class "RiskType"
, by class "asRisk"
.
signature(object = "asHampel")
:
accessor function for slot bound
.
signature(object = "asHampel")
Matthias Kohl [email protected]
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.
new("asHampel")
new("asHampel")
Generates an object of class "asMSE"
.
asMSE(biastype = symmetricBias(), normtype = NormType())
asMSE(biastype = symmetricBias(), normtype = NormType())
biastype |
a bias type of class |
normtype |
a norm type of class |
Object of class "asMSE"
Matthias Kohl [email protected]
Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.
asMSE() ## The function is currently defined as function(biastype = symmetricBias(), normtype = NormType()){ new("asMSE", biastype = biastype, normtype = normtype) }
asMSE() ## The function is currently defined as function(biastype = symmetricBias(), normtype = NormType()){ new("asMSE", biastype = biastype, normtype = normtype) }
Class of asymptotic mean square error.
Objects can be created by calls of the form new("asMSE", ...)
.
More frequently they are created via the generating function
asMSE
.
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
Class "asGRisk"
, directly.
Class "asRiskwithBias"
, by class "asGRisk"
.
Class "asRisk"
, by class "asRiskwithBias"
.
Class "RiskType"
, by class "asGRisk"
.
No methods defined with class "asMSE" in the signature.
Matthias Kohl [email protected]
Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.
new("asMSE")
new("asMSE")
Class of asymptotic risks.
A virtual Class: No objects may be created from it.
type
Object of class "character"
.
Class "RiskType"
, directly.
No methods defined with class "asRisk" in the signature.
Matthias Kohl [email protected]
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.
Class of asymptotic risks.
A “virtual” Class (although it does not contain "VIRTUAL"): No objects may be created from it.
type
Object of class "character"
.
biastype
Object of class "BiasType"
.
normtype
Object of class "NormType"
.
Class "RiskType"
, directly.
signature(object = "asRiskwithBias")
:
accessor function for slot biastype
.
signature(object = "asRiskwithBias", value = "BiasType")
:
replacement function for slot biastype
.
signature(object = "asRiskwithBias")
:
accessor function for slot normtype
.
signature(object = "asRiskwithBias", value = "NormType")
:
replacement function for slot normtype
.
signature(object = "asRiskwithBias")
:
accessor function for slot fct
of slot norm
.
Matthias Kohl [email protected], Peter Ruckdeschel [email protected]
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.
Generates an object of class "asSemivar"
.
asSemivar(sign = 1)
asSemivar(sign = 1)
sign |
positive (=1) or negative Bias (=-1) |
Object of class "asSemivar"
Peter Ruckdeschel [email protected]
Ruckdeschel, P. (2005) Optimally One-Sided Bounded Influence Curves. Mathematical Methods in Statistics 14(1), 105-131.
asSemivar()
asSemivar()
Class for semi-variance risk.
Objects can be created by calls of the form new("asSemivar", ...)
.
More frequently they are created via the generating function
asSemivar
.
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
signature(object = "asSemivar")
:
accessor function for slot sign
.
signature(object = "asSemivar", value = "numeric")
:
replacement function for slot sign
.
Class "asGRisk"
, directly.
Class "asRiskwithBias"
, by class "asGRisk"
.
Class "asRisk"
, by class "asRiskwithBias"
.
Class "RiskType"
, by class "asGRisk"
.
Peter Ruckdeschel [email protected]
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.
asSemivar()
asSemivar()
Generates an object of class "asUnOvShoot"
.
asUnOvShoot(width = 1.960, biastype = symmetricBias())
asUnOvShoot(width = 1.960, biastype = symmetricBias())
width |
positive real: half the width of given confidence interval. |
biastype |
a bias type of class |
Object of class "asUnOvShoot"
Matthias Kohl [email protected]
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.
asUnOvShoot() ## The function is currently defined as function(width = 1.960, biastype = symmetricBias()){ new("asUnOvShoot", width = width, biastype = biastype) }
asUnOvShoot() ## The function is currently defined as function(width = 1.960, biastype = symmetricBias()){ new("asUnOvShoot", width = width, biastype = biastype) }
Class of asymptotic under-/overshoot probability.
Objects can be created by calls of the form new("asUnOvShoot", ...)
.
More frequently they are created via the generating function
asUnOvShoot
.
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
Class "asGRisk"
, directly.
Class "asRiskwithBias"
, by class "asGRisk"
.
Class "asRisk"
, by class "asRiskwithBias"
.
Class "RiskType"
, by class "asGRisk"
.
signature(object = "asUnOvShoot")
:
accessor function for slot width
.
signature(object = "asUnOvShoot")
Matthias Kohl [email protected]
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.
new("asUnOvShoot")
new("asUnOvShoot")
Generates an object of class "asymmetricBias"
.
asymmetricBias(name = "asymmetric Bias", nu = c(1,1) )
asymmetricBias(name = "asymmetric Bias", nu = c(1,1) )
name |
name of the bias type |
nu |
weights for negative and positive bias, respectively |
Object of class "asymmetricBias"
Peter Ruckdeschel [email protected]
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.
asymmetricBias() ## The function is currently defined as function(){ new("asymmetricBias", name = "asymmetric Bias", nu = c(1,1)) }
asymmetricBias() ## The function is currently defined as function(){ new("asymmetricBias", name = "asymmetric Bias", nu = c(1,1)) }
Class of asymmetric bias types.
Objects can be created by calls of the form new("asymmetricBias", ...)
.
More frequently they are created via the generating function
asymmetricBias
.
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
signature(object = "asymmetricBias")
:
accessor function for slot nu
.
signature(object = "asymmetricBias", value = "numeric")
:
replacement function for slot nu
.
Class "BiasType"
, directly.
Peter Ruckdeschel [email protected]
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.
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)
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)
Generates an object of class "L2ParamFamily"
which
represents a Beta family.
BetaFamily(shape1 = 1, shape2 = 1, trafo, withL2derivDistr = TRUE)
BetaFamily(shape1 = 1, shape2 = 1, trafo, withL2derivDistr = TRUE)
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 |
The slots of the corresponding L2 differentiable parameteric family are filled.
Object of class "L2ParamFamily"
Peter Ruckdeschel [email protected]
L2ParamFamily-class
, Beta-class
(B1 <- BetaFamily()) FisherInfo(B1) ## IGNORE_RDIFF_BEGIN checkL2deriv(B1) ## IGNORE_RDIFF_END
(B1 <- BetaFamily()) FisherInfo(B1) ## IGNORE_RDIFF_BEGIN checkL2deriv(B1) ## IGNORE_RDIFF_END
Class of bias types.
A virtual Class: No objects may be created from it.
name
Object of class "character"
.
signature(object = "BiasType")
:
accessor function for slot name
.
signature(object = "BiasType", value = "character")
:
replacement function for slot name
.
Peter Ruckdeschel [email protected]
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.
aB <- positiveBias() name(aB)
aB <- positiveBias() name(aB)
Generates an object of class "L2ParamFamily"
which
represents a Binomial family where the probability of
success is the parameter of interest.
BinomFamily(size = 1, prob = 0.5, trafo)
BinomFamily(size = 1, prob = 0.5, trafo)
size |
number of trials |
prob |
probability of success |
trafo |
function in |
The slots of the corresponding L2 differentiable parameteric family are filled.
Object of class "L2ParamFamily"
Matthias Kohl [email protected]
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.
L2ParamFamily-class
, Binom-class
(B1 <- BinomFamily(size = 25, prob = 0.25)) plot(B1) FisherInfo(B1) checkL2deriv(B1)
(B1 <- BinomFamily(size = 25, prob = 0.25)) plot(B1) FisherInfo(B1) checkL2deriv(B1)
Generates an object of class "L2LocationFamily"
which
represents a Cauchy location family.
CauchyLocationFamily(loc = 0, scale = 1, trafo)
CauchyLocationFamily(loc = 0, scale = 1, trafo)
loc |
location |
scale |
scale |
trafo |
function in |
The slots of the corresponding L2 differentiable parameteric family are filled.
Object of class "L2LocationScaleFamily"
Peter Ruckdeschel [email protected]
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.
L2ParamFamily-class
, Cauchy-class
(C1 <- CauchyLocationFamily()) plot(C1) FisherInfo(C1) ### need smaller integration range: checkL2deriv(C1)
(C1 <- CauchyLocationFamily()) plot(C1) FisherInfo(C1) ### need smaller integration range: checkL2deriv(C1)
Generates an object of class "L2LocationScaleFamily"
which
represents a Cauchy location and scale family.
CauchyLocationScaleFamily(loc = 0, scale = 1, trafo)
CauchyLocationScaleFamily(loc = 0, scale = 1, trafo)
loc |
location |
scale |
scale |
trafo |
function in |
The slots of the corresponding L2 differentiable parameteric family are filled.
Object of class "L2LocationScaleFamily"
Matthias Kohl [email protected]
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.
L2ParamFamily-class
, Cauchy-class
(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)
(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 the L2-derivative of an L2-differentiable family of probability measures.
checkL2deriv(L2Fam, ...) ## S3 method for class 'relMatrix' print(x,...)
checkL2deriv(L2Fam, ...) ## S3 method for class 'relMatrix' print(x,...)
L2Fam |
L2-differentiable family of probability measures |
x |
argument to be printed |
... |
additional parameters (ignored/for compatibility with S3 generic
in case |
The precisions of the centering and the Fisher information are computed.
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.
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
.
Matthias Kohl [email protected]
Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.
F1 <- new("L2ParamFamily") checkL2deriv(F1)
F1 <- new("L2ParamFamily") checkL2deriv(F1)
Return value S4 classes for method “confint”.
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
.
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.
signature(object = "Confint")
:
accessor function for slot type
.
signature(object = "Confint", method = "missing")
:
accessor function for slot type
.
signature(object = "Confint")
:
accessor function for slot call.estimate
.
signature(object = "Confint")
:
accessor function for slot name.estimate
.
signature(object = "Confint")
:
accessor function for slot trafo.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
.
signature(object = "Confint")
:
accessor function for slot completecases.estimate
.
signature(object = "Confint")
:
accessor function for slot nuisance.estimate
.
signature(object = "Confint")
:
accessor function for slot fixed.estimate
.
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.
signature(object = "Confint")
: just as show
,
but with additional arguments digits
.
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.
The pretty-printing code for methods show
and print
has been borrowed from confint.default
in package stats.
Peter Ruckdeschel [email protected]
Estimator
, confint
, Estimate-class
,
trafo-methods
## 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")
## 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;
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.
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, ...)
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, ...)
object |
in default / signature |
parm |
only used in default / signature |
level |
the confidence level required. |
method |
not yet used (only as |
... |
additional argument(s) for methods. |
confint
is a generic function. Its behavior differs according to
its arguments.
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%).
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.
confint
,
confint.glm
and confint.nls
in
package MASS, Confint-class
.
## 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)
## 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)
Provides information on the (intended) masking of and (non-intended) masking by other other functions in package distrMod
distrModMASK(library = NULL)
distrModMASK(library = NULL)
library |
a character vector with path names of R libraries, or |
no value is returned
Peter Ruckdeschel [email protected]
## IGNORE_RDIFF_BEGIN distrModMASK() ## IGNORE_RDIFF_END
## IGNORE_RDIFF_BEGIN distrModMASK() ## IGNORE_RDIFF_END
With distrModOptions
you can inspect and change
the global variables of the package distrMod.
distrModOptions(...) getdistrModOption(x) distrModoptions(...)
distrModOptions(...) getdistrModOption(x) distrModoptions(...)
... |
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. |
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.
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
.
For compatibility with spelling in package distr, distrModoptions
is
just a synonym to distrModoptions
.
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"
.
Matthias Kohl [email protected],
Peter Ruckdeschel [email protected]
options
, getOption
,
distroptions
, getdistrOption
distrModoptions() distrModoptions("show.details") distrModoptions("show.details" = "maximal") distrModOptions("show.details" = "minimal") # or getdistrModOption("show.details")
distrModoptions() distrModoptions("show.details") distrModoptions("show.details" = "maximal") distrModOptions("show.details" = "minimal") # or getdistrModOption("show.details")
Class of estimates.
Objects can be created by calls of the form new("Estimate", ...)
.
More frequently they are created via the generating function
Estimator
.
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.
signature(object = "Estimate")
:
accessor function for slot name
.
signature(object = "Estimate")
:
replacement function for slot name
.
signature(object = "Estimate")
:
accessor function for slot estimate
.
signature(object = "Estimate")
:
accessor function for slot untransformed.estimate
.
signature(object = "Estimate")
:
accessor function for slot estimate.call
.
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
.
signature(object = "Estimate")
:
accessor function for slot completecases
.
signature(object = "Estimate")
:
accessor function for slot asvar
.
signature(object = "Estimate")
:
replacement function for slot asvar
.
signature(object = "Estimate")
:
accessor function for slot untransformed.asvar
.
signature(object = "Estimate")
:
accessor function for nuisance
part of slot estimate
.
signature(object = "Estimate")
:
accessor function for main
part of slot estimate
.
signature(object = "Estimate")
:
accessor function for slot fixed
.
signature(object = "Estimate")
:
accessor function for slot Infos
.
signature(object = "Estimate")
:
replacement function for slot Infos
.
signature(object = "Estimate")
:
function to add an information to slot Infos
.
signature(object = "Estimate")
signature(object = "Estimate")
: just as show
,
but with additional arguments digits
.
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
of the parameter
.
To be coherent with the corresponding nuisance implementation, we make the following convention:
The full parameter is split up coordinate-wise
in a main parameter
and a nuisance parameter
(which is unknown, too, hence has to be
estimated, but only is of secondary interest) and a fixed,
known part
.
Without loss of generality, we restrict ourselves to the case that
transformation only acts on the main parameter
— if we want to transform the whole
parameter, we only have to assume that both nuisance parameter
and fixed, known part of the parameter
have length 0.
To the implementation:
Slot trafo
can either contain a (constant) matrix
or a function
mapping main parameter
to some range
.
If slot value trafo
is a function, besides ,
it will also return the corresponding derivative matrix
.
More specifically, the return value of this function
theta
is a
list with entries fval
, the function value ,
and
mat
, the derivative matrix.
In case trafo
is a matrix , we interpret it as such a derivative
matrix
,
and, correspondingly,
as the linear mapping
.
The pretty-printing code for methods show
and print
has been borrowed from print.fitdistr
in package MASS by B.D. Ripley.
Matthias Kohl [email protected],
Peter Ruckdeschel [email protected]
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)
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)
The function Estimator
provides a general way to compute
estimates.
Estimator(x, estimator, name, Infos, asvar = NULL, nuis.idx, trafo = NULL, fixed = NULL, asvar.fct, na.rm = TRUE, ..., ParamFamily = NULL, .withEvalAsVar = TRUE)
Estimator(x, estimator, name, Infos, asvar = NULL, nuis.idx, trafo = NULL, fixed = NULL, asvar.fct, na.rm = TRUE, ..., ParamFamily = NULL, .withEvalAsVar = TRUE)
x |
(empirical) data |
estimator |
function: estimator to be evaluated on |
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 |
asvar.fct |
optionally: a function to determine the corresponding
asymptotic variance; if given, |
na.rm |
logical: if |
... |
further arguments to |
ParamFamily |
an optional object of class |
.withEvalAsVar |
logical: shall slot |
The argument criterion
has to be a function with arguments the
empirical data as well as an object of class "Distribution"
and possibly ...
.
An object of S4-class "Estimate"
.
Matthias Kohl [email protected],
Peter Ruckdeschel [email protected]
x <- rnorm(100) Estimator(x, estimator = mean, name = "mean") X <- matrix(rnorm(1000), nrow = 10) Estimator(X, estimator = rowMeans, name = "mean")
x <- rnorm(100) Estimator(x, estimator = mean, name = "mean") X <- matrix(rnorm(1000), nrow = 10) Estimator(X, estimator = rowMeans, name = "mean")
Generates an object of class "EvenSymmetric"
.
EvenSymmetric(SymmCenter = 0)
EvenSymmetric(SymmCenter = 0)
SymmCenter |
numeric: center of symmetry |
Object of class "EvenSymmetric"
Matthias Kohl [email protected]
EvenSymmetric-class
, FunctionSymmetry-class
EvenSymmetric() ## The function is currently defined as function(SymmCenter = 0){ new("EvenSymmetric", SymmCenter = SymmCenter) }
EvenSymmetric() ## The function is currently defined as function(SymmCenter = 0){ new("EvenSymmetric", SymmCenter = SymmCenter) }
Class for even functions.
Objects can be created by calls of the form new("EvenSymmetric")
.
More frequently they are created via the generating function
EvenSymmetric
.
type
Object of class "character"
:
contains “even function”
SymmCenter
Object of class "numeric"
:
center of symmetry
Class "FunctionSymmetry"
, directly.
Class "Symmetry"
, by class "FunctionSymmetry"
.
Matthias Kohl [email protected]
EvenSymmetric
, FunctionSymmetry-class
new("EvenSymmetric")
new("EvenSymmetric")
existsPIC-methods to check whether in a given L2 differentiable model at parameter value theta there exist
(partial) influence curves to Trafo .
existsPIC(object, ...) ## S4 method for signature 'L2ParamFamily' existsPIC(object, warning = TRUE, tol = .Machine$double.eps^.5)
existsPIC(object, ...) ## S4 method for signature 'L2ParamFamily' existsPIC(object, warning = TRUE, tol = .Machine$double.eps^.5)
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 |
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
for
and
], it suffices to check that
is a subset of
. This is done by
a call to
isKerAinKerB
.
Peter Ruckdeschel [email protected]
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.
Generates an object of class "L2ScaleFamily"
which
represents an exponential scale family.
ExpScaleFamily(scale = 1, trafo)
ExpScaleFamily(scale = 1, trafo)
scale |
scale (= 1/rate) |
trafo |
function in |
The slots of the corresponding L2 differentiable
parameteric family are filled. The scale parameter corresponds
to .
Object of class "L2ScaleFamily"
Matthias Kohl [email protected]
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.
L2ParamFamily-class
, Exp-class
(E1 <- ExpScaleFamily()) plot(E1) Map(L2deriv(E1)[[1]]) ## IGNORE_RDIFF_BEGIN checkL2deriv(E1) ## IGNORE_RDIFF_END
(E1 <- ExpScaleFamily()) plot(E1) Map(L2deriv(E1)[[1]]) ## IGNORE_RDIFF_BEGIN checkL2deriv(E1) ## IGNORE_RDIFF_END
Generates an object of class "fiBias"
.
fiBias()
fiBias()
Object of class "fiBias"
Matthias Kohl [email protected]
Ruckdeschel, P. and Kohl, M. (2005) How to approximate the finite sample risk of M-estimators.
fiBias() ## The function is currently defined as function(){ new("fiBias") }
fiBias() ## The function is currently defined as function(){ new("fiBias") }
Class of finite-sample bias.
Objects can be created by calls of the form new("fiBias", ...)
.
More frequently they are created via the generating function
fiBias
.
type
Object of class "character"
:
“finite-sample bias”.
Class "fiRisk"
, directly.
Class "RiskType"
, by class "fiRisk"
.
No methods defined with class "fiBias" in the signature.
Matthias Kohl [email protected]
Ruckdeschel, P. and Kohl, M. (2005) How to approximate the finite sample risk of M-estimators.
new("fiBias")
new("fiBias")
Generates an object of class "fiCov"
.
fiCov()
fiCov()
Object of class "fiCov"
Matthias Kohl [email protected]
Ruckdeschel, P. and Kohl, M. (2005) How to approximate the finite sample risk of M-estimators.
fiCov() ## The function is currently defined as function(){ new("fiCov") }
fiCov() ## The function is currently defined as function(){ new("fiCov") }
Class of finite-sample covariance.
Objects can be created by calls of the form new("fiCov", ...)
.
More frequently they are created via the generating function
fiCov
.
type
Object of class "character"
:
“finite-sample covariance”.
Class "fiRisk"
, directly.
Class "RiskType"
, by class "fiRisk"
.
No methods defined with class "fiCov" in the signature.
Matthias Kohl [email protected]
Ruckdeschel, P. and Kohl, M. (2005) How to approximate the finite sample risk of M-estimators.
new("fiCov")
new("fiCov")
Generates an object of class "fiHampel"
.
fiHampel(bound = Inf)
fiHampel(bound = Inf)
bound |
positive real: bias bound |
Object of class fiHampel
Matthias Kohl [email protected]
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.
fiHampel() ## The function is currently defined as function(bound = Inf){ new("fiHampel", bound = bound) }
fiHampel() ## The function is currently defined as function(bound = Inf){ new("fiHampel", bound = bound) }
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 can be created by calls of the form new("fiHampel", ...)
.
More frequently they are created via the generating function
fiHampel
.
type
Object of class "character"
:
“trace of finite-sample covariance for given bias bound”.
bound
Object of class "numeric"
:
given positive bias bound.
Class "fiRisk"
, directly.
Class "RiskType"
, by class "fiRisk"
.
signature(object = "fiHampel")
:
accessor function for slot bound
.
signature(object = "fiHampel")
Matthias Kohl [email protected]
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.
new("fiHampel")
new("fiHampel")
Generates an object of class "fiMSE"
.
fiMSE()
fiMSE()
Object of class "fiMSE"
Matthias Kohl [email protected]
Ruckdeschel, P. and Kohl, M. (2005) How to approximate the finite sample risk of M-estimators.
fiMSE() ## The function is currently defined as function(){ new("fiMSE") }
fiMSE() ## The function is currently defined as function(){ new("fiMSE") }
Class of asymptotic mean square error.
Objects can be created by calls of the form new("fiMSE", ...)
.
More frequently they are created via the generating function
fiMSE
.
type
Object of class "character"
:
“finite-sample mean square error”.
Class "fiRisk"
, directly.
Class "RiskType"
, by class "fiRisk"
.
No methods defined with class "fiMSE" in the signature.
Matthias Kohl [email protected]
Ruckdeschel, P. and Kohl, M. (2005) How to approximate the finite sample risk of M-estimators.
new("fiMSE")
new("fiMSE")
Class of finite-sample risks.
A virtual Class: No objects may be created from it.
type
Object of class "character"
.
Class "RiskType"
, directly.
No methods defined with class "fiRisk" in the signature.
Matthias Kohl [email protected]
Ruckdeschel, P. and Kohl, M. (2005) How to approximate the finite sample risk of M-estimators.
Generates an object of class "fiUnOvShoot"
.
fiUnOvShoot(width = 1.960)
fiUnOvShoot(width = 1.960)
width |
positive real: half the width of given confidence interval. |
Object of class "fiUnOvShoot"
Matthias Kohl [email protected]
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.
fiUnOvShoot() ## The function is currently defined as function(width = 1.960){ new("fiUnOvShoot", width = width) }
fiUnOvShoot() ## The function is currently defined as function(width = 1.960){ new("fiUnOvShoot", width = width) }
Class of finite-sample under-/overshoot probability.
Objects can be created by calls of the form new("fiUnOvShoot", ...)
.
More frequently they are created via the generating function
fiUnOvShoot
.
type
Object of class "character"
:
“finite-sample under-/overshoot probability”.
width
Object of class "numeric"
:
half the width of given confidence interval.
Class "fiRisk"
, directly.
Class "RiskType"
, by class "fiRisk"
.
signature(object = "fiUnOvShoot")
:
accessor function for slot width
.
signature(object = "fiUnOvShoot")
Matthias Kohl [email protected]
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.
new("fiUnOvShoot")
new("fiUnOvShoot")
Class of symmetries for functions.
A virtual Class: No objects may be created from it.
type
Object of class "character"
:
discribes type of symmetry.
SymmCenter
Object of class "OptionalNumeric"
:
center of symmetry.
Class "Symmetry"
, directly.
Matthias Kohl [email protected]
Symmetry-class
, OptionalNumeric-class
Generates an object of class "FunSymmList"
.
FunSymmList(...)
FunSymmList(...)
... |
Objects of class |
Object of class "FunSymmList"
Matthias Kohl [email protected]
FunSymmList(NonSymmetric(), EvenSymmetric(SymmCenter = 1), OddSymmetric(SymmCenter = 2)) ## The function is currently defined as function (...){ new("FunSymmList", list(...)) }
FunSymmList(NonSymmetric(), EvenSymmetric(SymmCenter = 1), OddSymmetric(SymmCenter = 2)) ## The function is currently defined as function (...){ new("FunSymmList", list(...)) }
Create a list of symmetries for a list of functions
Objects can be created by calls of the form new("FunSymmList", ...)
.
More frequently they are created via the generating function
FunSymmList
.
.Data
Object of class "list"
. A list
of objects of class "FunctionSymmetry"
.
Class "list"
, from data part.
Class "vector"
, by class "list"
.
Matthias Kohl [email protected]
new("FunSymmList", list(NonSymmetric(), EvenSymmetric(SymmCenter = 1), OddSymmetric(SymmCenter = 2)))
new("FunSymmList", list(NonSymmetric(), EvenSymmetric(SymmCenter = 1), OddSymmetric(SymmCenter = 2)))
Generates an object of class "L2ParamFamily"
which
represents a Gamma family.
GammaFamily(scale = 1, shape = 1, trafo, withL2derivDistr = TRUE)
GammaFamily(scale = 1, shape = 1, trafo, withL2derivDistr = TRUE)
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 |
The slots of the corresponding L2 differentiable parameteric family are filled.
Object of class "L2ParamFamily"
Matthias Kohl [email protected]
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.
L2ParamFamily-class
, Gammad-class
(G1 <- GammaFamily()) FisherInfo(G1) ## IGNORE_RDIFF_BEGIN checkL2deriv(G1) ## IGNORE_RDIFF_END
(G1 <- GammaFamily()) FisherInfo(G1) ## IGNORE_RDIFF_BEGIN checkL2deriv(G1) ## IGNORE_RDIFF_END
Generates an object of class "InfoNorm"
—
used for information-standardized influence curves.
InfoNorm()
InfoNorm()
Object of class "InfoNorm"
Matthias Kohl [email protected]
Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.
## IGNORE_RDIFF_BEGIN InfoNorm() ## The function is currently defined as function(){ new("InfoNorm") } ## IGNORE_RDIFF_END
## IGNORE_RDIFF_BEGIN InfoNorm() ## The function is currently defined as function(){ new("InfoNorm") } ## IGNORE_RDIFF_END
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 entails
Bx=0
.
isKerAinKerB(A, B, tol = .Machine$double.eps)
isKerAinKerB(A, B, tol = .Machine$double.eps)
A |
a matrix; if |
B |
a matrix; if |
tol |
the tolerance for detecting linear dependencies in the
columns of |
via calls to svd
, the projectors and
onto the respective orthogonal complements of
and
are calculated and then is checked whether
.
logical
Peter Ruckdeschel [email protected]
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
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
Class of L2 differentiable parametric group families.
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
.
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.
Class "L2ParamFamily"
, directly.
Class "ParamFamily"
, by class "L2ParamFamily"
.
Class "ProbFamily"
, by class "ParamFamily"
.
signature(object = "L2GroupParamFamily")
:
accessor function for slot LogDeriv
.
signature(object = "L2GroupParamFamily")
:
replacement function for slot LogDeriv
.
Peter Ruckdeschel [email protected]
Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.
L2ParamFamily-class
, ParamFamily-class
F1 <- new("L2GroupParamFamily") plot(F1)
F1 <- new("L2GroupParamFamily") plot(F1)
Generates an object of class "L2LocationFamily"
.
L2LocationFamily(loc = 0, name, centraldistribution = Norm(), locname = "loc", modParam, LogDeriv, L2derivDistr.0, FisherInfo.0, distrSymm, L2derivSymm, L2derivDistrSymm, trafo, .returnClsName = NULL)
L2LocationFamily(loc = 0, name, centraldistribution = Norm(), locname = "loc", modParam, LogDeriv, L2derivDistr.0, FisherInfo.0, distrSymm, L2derivSymm, L2derivDistrSymm, trafo, .returnClsName = NULL)
loc |
numeric: location parameter of the model. |
name |
character: name of the parametric family. |
centraldistribution |
object of class |
modParam |
optional function: mapping from the parameter space
(represented by |
locname |
a character vector of length 1 containing the name of the location parameter |
LogDeriv |
function with argument |
L2derivDistr.0 |
object of class |
FisherInfo.0 |
object of class |
distrSymm |
object of class |
L2derivSymm |
object of class |
L2derivDistrSymm |
object of class |
trafo |
matrix or function in |
.returnClsName |
the class name of the return value; by default this
argument is |
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.
Object of class "L2LocationFamily"
Matthias Kohl [email protected],
Peter Ruckdeschel [email protected]
Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.
F1 <- L2LocationFamily() plot(F1)
F1 <- L2LocationFamily() plot(F1)
Class of L2 differentiable parametric group families.
Objects can be created by calls of the form new("L2LocationFamily", ...)
.
More frequently they are created via the generating function
L2LocationFamily
.
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
Class "L2LocationScaleUnion"
, directly.
Class "L2GroupParamFamily"
, by class "L2LocationScaleUnion"
.
Class "L2ParamFamily"
, by class "L2GroupParamFamily"
.
Class "ParamFamily"
, by class "L2ParamFamily"
.
Class "ProbFamily"
, by class "ParamFamily"
.
signature(model = "L2LocationFamily", param = "ParamFamParameter")
:
moves the L2-location family model
to parameter param
Matthias Kohl [email protected],
Peter Ruckdeschel [email protected]
Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.
L2LocationFamily
, ParamFamily-class
F1 <- new("L2LocationFamily") plot(F1)
F1 <- new("L2LocationFamily") plot(F1)
Generates an object of class "L2LocationScaleFamily"
.
L2LocationScaleFamily(loc = 0, scale = 1, name, centraldistribution = Norm(), locscalename = c("loc", "scale"), modParam, LogDeriv, L2derivDistr.0, FisherInfo.0, distrSymm, L2derivSymm, L2derivDistrSymm, trafo, .returnClsName = NULL)
L2LocationScaleFamily(loc = 0, scale = 1, name, centraldistribution = Norm(), locscalename = c("loc", "scale"), modParam, LogDeriv, L2derivDistr.0, FisherInfo.0, distrSymm, L2derivSymm, L2derivDistrSymm, trafo, .returnClsName = NULL)
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 |
modParam |
optional function: mapping from the parameter space
(represented by |
locscalename |
a character vector of length 2 containing the names
of the location and scale parameter; either unnamed, then order must
be |
LogDeriv |
function with argument |
L2derivDistr.0 |
list of length 2 of objects of class |
FisherInfo.0 |
object of class |
distrSymm |
object of class |
L2derivSymm |
object of class |
L2derivDistrSymm |
object of class |
trafo |
matrix or function in |
.returnClsName |
the class name of the return value; by default this
argument is |
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.
Object of class "L2LocationScaleFamily"
Matthias Kohl [email protected],
Peter Ruckdeschel [email protected]
Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.
F1 <- L2LocationScaleFamily() plot(F1)
F1 <- L2LocationScaleFamily() plot(F1)
Class of L2 differentiable parametric group families.
Objects can be created by calls of the form new("L2LocationScaleFamily", ...)
.
More frequently they are created via the generating function
L2LocationScaleFamily
.
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
Class "L2LocationScaleUnion"
, directly.
Class "L2GroupParamFamily"
, by class "L2LocationScaleUnion"
.
Class "L2ParamFamily"
, by class "L2GroupParamFamily"
.
Class "ParamFamily"
, by class "L2ParamFamily"
.
Class "ProbFamily"
, by class "ParamFamily"
.
signature(model = "L2LocationScaleFamily", param = "ParamFamParameter")
:
moves the L2-location and scale family model
to parameter param
Matthias Kohl [email protected],
Peter Ruckdeschel [email protected]
Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.
L2LocationScaleFamily
, ParamFamily-class
F1 <- new("L2LocationScaleFamily") plot(F1)
F1 <- new("L2LocationScaleFamily") plot(F1)
Generates an object of class "L2LocationScaleFamily"
in the situation
where location is main, scale nuisance parameter.
L2LocationUnknownScaleFamily(loc = 0, scale = 1, name, centraldistribution = Norm(), locscalename = c("loc", "scale"), modParam, LogDeriv, L2derivDistr.0, FisherInfo.0, distrSymm, L2derivSymm, L2derivDistrSymm, trafo, .returnClsName = NULL)
L2LocationUnknownScaleFamily(loc = 0, scale = 1, name, centraldistribution = Norm(), locscalename = c("loc", "scale"), modParam, LogDeriv, L2derivDistr.0, FisherInfo.0, distrSymm, L2derivSymm, L2derivDistrSymm, trafo, .returnClsName = NULL)
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 |
modParam |
optional function: mapping from the parameter space
(represented by |
locscalename |
a character vector of length 2 containing the names
of the location and scale parameter; either unnamed, then order must
be |
LogDeriv |
function with argument |
L2derivDistr.0 |
list of length 2 of objects of class |
FisherInfo.0 |
object of class |
distrSymm |
object of class |
L2derivSymm |
object of class |
L2derivDistrSymm |
object of class |
trafo |
matrix or function in |
.returnClsName |
the class name of the return value; by default this
argument is |
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.
Object of class "L2LocationScaleFamily"
Peter Ruckdeschel [email protected]
Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.
F1 <- L2LocationUnknownScaleFamily() plot(F1)
F1 <- L2LocationUnknownScaleFamily() plot(F1)
Generates an object of class "L2ParamFamily"
.
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)
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)
name |
character string: name of the family |
distribution |
object of class |
distrSymm |
object of class |
main |
numeric vector: main parameter |
nuisance |
numeric vector: nuisance parameter |
fixed |
numeric vector: fixed part of the parameter |
trafo |
function in |
param |
object of class |
startPar |
|
makeOKPar |
|
modifyParam |
function: mapping from the parameter space
(represented by |
props |
character vector: properties of the family |
L2deriv.fct |
function: mapping from the parameter space (argument
|
L2derivSymm |
object of class |
L2derivDistr |
object of class |
L2derivDistrSymm |
object of class |
FisherInfo.fct |
function: mapping from the parameter space (argument
|
FisherInfo |
object of class |
.returnClsName |
the class name of the return value; by default this
argument is |
.withMDE |
logical of length 1: Tells R how to use the function from
slot |
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
.
Object of class "L2ParamFamily"
Matthias Kohl [email protected],
Peter Ruckdeschel [email protected]
Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.
F1 <- L2ParamFamily() plot(F1)
F1 <- L2ParamFamily() plot(F1)
Class of L2 differentiable parametric families.
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 can be created by calls of the form new("L2ParamFamily", ...)
.
More frequently they are created via the generating function
L2ParamFamily
.
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
.
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
.
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
.
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.
Class "ParamFamily"
, directly.
Class "ProbFamily"
, by class "ParamFamily"
.
signature(object = "L2ParamFamily")
:
accessor function for L2deriv
.
signature(object = "L2ParamFamily",
param = "ParamFamParameter")
:
returns the L2derivative at param
, i.e.
evaluates slot function L2deriv.fct
at param
.
signature(object = "L2ParamFamily")
:
accessor function for L2derivSymm
.
signature(object = "L2ParamFamily")
:
accessor function for L2derivDistr
.
signature(object = "L2ParamFamily")
:
accessor function for L2derivDistrSymm
.
signature(object = "L2ParamFamily")
:
accessor function for FisherInfo
.
signature(object = "L2ParamFamily",
param = "ParamFamParameter")
:
returns the Fisher Information at param
, i.e.
evaluates slot function FisherInfo.fct
at param
.
signature(object = "L2ParamFamily")
:
check centering of L2deriv
and compute precision
of Fisher information.
signature(object = "L2ParamFamily", fun = "EuclRandVariable", cond = "missing")
:
expectation of fun
under the distribution of object
.
signature(object = "L2ParamFamily", fun = "EuclRandMatrix", cond = "missing")
:
expectation of fun
under the distribution of object
.
signature(object = "L2ParamFamily", fun = "EuclRandVarList", cond = "missing")
:
expectation of fun
under the distribution of object
.
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
object of class "L2ParamFamily"
logical: if TRUE
(for working with Sweave
)
no extra device is opened and height/width are not set
logical: is a main title to be used? or
just as argument main
in plot.default
.
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
.
logical: is a sub-title to be used? or
just as argument sub
in plot.default
.
top margin – useful for non-standard main title sizes
bottom margin – useful for non-standard sub title sizes
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.
character or integer code; color for the inner title
shall default partition in panels be used —
defaults to TRUE
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.
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.
signature(model = "L2ParamFamily", param = "ParamFamParameter")
:
moves the L2-parametric Family model
to parameter param
Matthias Kohl [email protected],
Peter Ruckdeschel [email protected]
Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.
L2ParamFamily
, ParamFamily-class
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"))
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"))
Generates an object of class "L2ScaleFamily"
.
L2ScaleFamily(scale = 1, loc = 0, name, centraldistribution = Norm(), locscalename = c("loc", "scale"), modParam, LogDeriv, L2derivDistr.0, FisherInfo.0, distrSymm, L2derivSymm, L2derivDistrSymm, trafo, .returnClsName = NULL)
L2ScaleFamily(scale = 1, loc = 0, name, centraldistribution = Norm(), locscalename = c("loc", "scale"), modParam, LogDeriv, L2derivDistr.0, FisherInfo.0, distrSymm, L2derivSymm, L2derivDistrSymm, trafo, .returnClsName = NULL)
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 |
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,
|
modParam |
optional function: mapping from the parameter space
(represented by |
LogDeriv |
function with argument |
L2derivDistr.0 |
object of class |
FisherInfo.0 |
object of class |
distrSymm |
object of class |
L2derivSymm |
object of class |
L2derivDistrSymm |
object of class |
trafo |
matrix or function in |
.returnClsName |
the class name of the return value; by default this
argument is |
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.
Object of class "L2ScaleFamily"
Matthias Kohl [email protected],
Peter Ruckdeschel [email protected]
Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.
F1 <- L2ScaleFamily() plot(F1)
F1 <- L2ScaleFamily() plot(F1)
Class of L2 differentiable parametric group families.
Objects can be created by calls of the form new("L2ScaleFamily", ...)
.
More frequently they are created via the generating function
L2ScaleFamily
.
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
Class "L2LocationScaleUnion"
, directly.
Class "L2GroupParamFamily"
, by class "L2LocationScaleUnion"
.
Class "L2ParamFamily"
, by class "L2GroupParamFamily"
.
Class "ParamFamily"
, by class "L2ParamFamily"
.
Class "ProbFamily"
, by class "ParamFamily"
.
signature(model = "L2ScaleFamily", param = "ParamFamParameter")
:
moves the L2-scale family model
to parameter param
Matthias Kohl [email protected],
Peter Ruckdeschel [email protected]
Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.
L2ScaleFamily
, ParamFamily-class
F1 <- new("L2ScaleFamily") plot(F1)
F1 <- new("L2ScaleFamily") plot(F1)
Generates an object of class "L2LocationScaleFamily"
in the situation where scale is main, location nuisance parameter.
L2ScaleUnknownLocationFamily(loc = 0, scale = 1, name, centraldistribution = Norm(), locscalename = c("loc", "scale"), modParam, LogDeriv, L2derivDistr.0, FisherInfo.0, distrSymm, L2derivSymm, L2derivDistrSymm, trafo, .returnClsName = NULL)
L2ScaleUnknownLocationFamily(loc = 0, scale = 1, name, centraldistribution = Norm(), locscalename = c("loc", "scale"), modParam, LogDeriv, L2derivDistr.0, FisherInfo.0, distrSymm, L2derivSymm, L2derivDistrSymm, trafo, .returnClsName = NULL)
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 |
modParam |
optional function: mapping from the parameter space
(represented by |
locscalename |
a character vector of length 2 containing the names
of the location and scale parameter; either unnamed, then order must
be |
LogDeriv |
function with argument |
L2derivDistr.0 |
list of length 2 of objects of class |
FisherInfo.0 |
object of class |
distrSymm |
object of class |
L2derivSymm |
object of class |
L2derivDistrSymm |
object of class |
trafo |
matrix or function in |
.returnClsName |
the class name of the return value; by default this
argument is |
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.
Object of class "L2LocationScaleFamily"
Peter Ruckdeschel [email protected]
Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.
F1 <- L2ScaleUnknownLocationFamily() plot(F1)
F1 <- L2ScaleUnknownLocationFamily() plot(F1)
Generates an object of class "L2ScaleFamily"
which
represents a lognormal scale family.
LnormScaleFamily(meanlog = 0, sdlog = 1, trafo)
LnormScaleFamily(meanlog = 0, sdlog = 1, trafo)
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 |
The slots of the corresponding L2 differentiable parameteric family are filled.
Object of class "L2ScaleFamily"
Matthias Kohl [email protected]
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.
L2ParamFamily-class
, Lnorm-class
(L1 <- LnormScaleFamily()) plot(L1) Map(L2deriv(L1)[[1]]) checkL2deriv(L1)
(L1 <- LnormScaleFamily()) plot(L1) Map(L2deriv(L1)[[1]]) checkL2deriv(L1)
Generates an object of class "L2LocationScaleFamily"
which
represents a normal location and scale family.
LogisticLocationScaleFamily(location = 0, scale = 1, trafo) LOGISTINT2
LogisticLocationScaleFamily(location = 0, scale = 1, trafo) LOGISTINT2
location |
location |
scale |
scale |
trafo |
function in |
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
.
Object of class "L2LocationScaleFamily"
Peter Ruckdeschel [email protected]
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.
L2ParamFamily-class
, Logis-class
(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)
(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;
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, ...)
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, ...)
x |
numeric; data at which to evaluate the estimator |
PFam |
an object of class |
criterion |
a function measuring the “goodness of fit” |
startPar |
in case |
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 |
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 |
... |
additional argument(s) for |
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.
a list with components
estimate |
— the estimate as a named vector of |
criterion |
— the criterion value (i.e.; a |
est.name |
— the name of the estimator |
param |
— estimate coerced to class |
crit.fct |
— a function with the named components of |
method |
— a character reporting how the estimate was obtained, i.e.,
by |
crit.name |
character; the name of the criterion; may be |
Infos |
matrix; info slot to be filled in object of class |
samplesize |
numeric; sample size of |
Class of minimum criterion estimates.
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).
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
.
Class "Estimate"
, directly.
signature(object = "MCEstimate")
:
accessor function for slot criterion
.
signature(object = "MCEstimate")
:
replacement function for slot criterion
.
signature(object = "MCEstimate")
:
accessor function for slot optimwarn
.
signature(object = "MCEstimate")
:
accessor function for slot optimReturn
.
signature(object = "MCEstimate")
:
accessor function for slot startPar
.
signature(object = "MCEstimate")
:
accessor function for slot criterion.fct
.
signature(object = "Estimate")
signature(from = "MCEstimate", to = "mle")
:
create a "mle"
object from a "MCEstimate"
object
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.
Matthias Kohl [email protected],
Peter Ruckdeschel [email protected]
Estimate-class
, MCEstimator
,
MDEstimator
, MLEstimator
## (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
## (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
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.
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)
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)
x |
(empirical) data |
ParamFamily |
object of class |
criterion |
function: criterion to minimize; see Details section. |
crit.name |
optional name for criterion. |
startPar |
initial information used by |
Infos |
character: optional informations about estimator |
trafo |
an object of class |
penalty |
(non-negative) numeric: penalizes non valid parameter-values |
validity.check |
logical: shall return parameter value be checked for
validity? Defaults to yes ( |
asvar.fct |
optionally: a function to determine the corresponding
asymptotic variance; if given, |
na.rm |
logical: if |
... |
further arguments to |
.withEvalAsVar |
logical: shall slot |
nmsffx |
character: a potential suffix to be appended to the estimator name. |
.with.checkEstClassForParamFamily |
logical: Should a the end of the
function |
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.
An object of S4-class "MCEstimate"
which inherits from class
"Estimate"
.
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.
Matthias Kohl [email protected],
Peter Ruckdeschel [email protected]
ParamFamily-class
, ParamFamily
,
MCEstimate-class
## (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")
## (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")
The function MDEstimator
provides a general way to compute
minimum distance estimates.
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,... )
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,... )
x |
(empirical) data |
ParamFamily |
object of class |
distance |
(generic) function: to compute distance beetween (emprical)
data and objects of class |
dist.name |
optional name of distance |
muDatOrMod |
a character string specifying whether
as integration measure |
mu |
optional integration (probability) measure for CvM MDE.
defaults to |
paramDepDist |
logical; will computation of distance be parameter
dependent (see also note below)? if |
startPar |
initial information used by |
Infos |
character: optional informations about estimator |
trafo |
an object of class |
penalty |
(non-negative) numeric: penalizes non valid parameter-values |
validity.check |
logical: shall return parameter value be checked for
validity? Defaults to yes ( |
asvar.fct |
optionally: a function to determine the corresponding
asymptotic variance; if given, |
na.rm |
logical: if |
... |
for the estimators: further arguments to |
.withEvalAsVar |
logical: shall slot |
nmsffx |
character: a potential suffix to be appended to the estimator name. |
e1 |
object of class |
e2 |
object of class |
.with.checkEstClassForParamFamily |
logical: Should a the end of the
function |
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 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
.
The estimators return an object of S4-class "MCEstimate"
which inherits from class
"Estimate"
. CvMDist2
returns the respective distance.
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).
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.
Matthias Kohl [email protected],
Peter Ruckdeschel [email protected]
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.
ParamFamily-class
, ParamFamily
,
MCEstimator
, MCEstimate-class
,
fitdistr
## (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")
## (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 to produce consistent lists to be digested
in functions mceCalc
and mleCalc
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)
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)
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 |
crit.fct |
a function to fill slot |
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 |
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 |
optReturn |
object of class |
... |
further arguments to be passed
to |
object |
numeric; the data at which to evaluate the estimate |
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)
.
meRes |
a list of prescribed structure to be digested in functions
|
get.criterion.fct |
a function; see details below; |
samplesize |
numeric |
Peter Ruckdeschel [email protected]
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.
MLEstimator(x, ParamFamily, startPar = NULL, Infos, trafo = NULL, penalty = 1e20, validity.check = TRUE, na.rm = TRUE, ..., .withEvalAsVar = TRUE, dropZeroDensity = TRUE, nmsffx = "", .with.checkEstClassForParamFamily = TRUE)
MLEstimator(x, ParamFamily, startPar = NULL, Infos, trafo = NULL, penalty = 1e20, validity.check = TRUE, na.rm = TRUE, ..., .withEvalAsVar = TRUE, dropZeroDensity = TRUE, nmsffx = "", .with.checkEstClassForParamFamily = TRUE)
x |
(empirical) data |
ParamFamily |
object of class |
startPar |
initial information used by |
Infos |
character: optional informations about estimator |
trafo |
an object of class |
penalty |
(non-negative) numeric: penalizes non valid parameter-values |
validity.check |
logical: shall return parameter value be checked for
validity? Defaults to yes ( |
na.rm |
logical: if |
... |
further arguments to |
.withEvalAsVar |
logical: shall slot |
dropZeroDensity |
logical of length 1; shall observations with
density zero be dropped? Optimizers like |
nmsffx |
character: a potential suffix to be appended to the estimator name. |
.with.checkEstClassForParamFamily |
logical: Should a the end of the
function |
The function uses mleCalc
for method dispatch; this method by default
calls mceCalc
using the negative log-likelihood
as criterion which should be minimized.
An object of S4-class "MCEstimate"
which inherits from class
"Estimate"
.
Matthias Kohl [email protected],
Peter Ruckdeschel [email protected]
ParamFamily-class
, ParamFamily
,
MCEstimator
, MCEstimate-class
,
fitdistr
, mle
############################# ## 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)
############################# ## 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;
modifyModel
moves a model from one parameter value to
another.
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, ...)
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, ...)
model |
an object of class |
param |
an object of class |
.withCall |
logical: shall slot |
.withL2derivDistr |
logical: shall slot |
... |
additional argument(s) for methods; not used so far |
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.
a corresponding instance of the model in argument model
with moved
parameters.
Generates an object of class "L2ParamFamily"
which
represents a Nbinomial family where the probability of
success is the parameter of interest.
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 )
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 )
size |
number of trials |
prob |
probability of success |
mean |
alternative parameter for negative binomial parameter |
trafo |
function in |
withL2derivDistr |
logical: shall the distribution of the L2 derivative
be computed? Defaults to |
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.
Object of class "L2ParamFamily"
Peter Ruckdeschel [email protected]
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.
L2ParamFamily-class
, Nbinom-class
(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)
(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)
Generates an object of class "onesidedBias"
.
negativeBias(name = "negative Bias")
negativeBias(name = "negative Bias")
name |
name of the bias type |
Object of class "onesidedBias"
Peter Ruckdeschel [email protected]
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.
negativeBias() ## The function is currently defined as function(){ new("onesidedBias", name = "negative Bias", sign = -1) }
negativeBias() ## The function is currently defined as function(){ new("onesidedBias", name = "negative Bias", sign = -1) }
Generates an object of class "NonSymmetric"
.
NonSymmetric()
NonSymmetric()
Object of class "NonSymmetric"
Matthias Kohl [email protected]
NonSymmetric-class
, FunctionSymmetry-class
NonSymmetric() ## The function is currently defined as function(){ new("NonSymmetric") }
NonSymmetric() ## The function is currently defined as function(){ new("NonSymmetric") }
Class for non-symmetric functions.
Objects can be created by calls of the form new("NonSymmetric")
.
More frequently they are created via the generating function
NonSymmetric
.
type
Object of class "character"
:
contains “non-symmetric function”
SymmCenter
Object of class "NULL"
Class "FunctionSymmetry"
, directly.
Class "Symmetry"
, by class "FunctionSymmetry"
.
Matthias Kohl [email protected]
new("NonSymmetric")
new("NonSymmetric")
Functions to determine certain norms.
EuclideanNorm(x) QuadFormNorm(x,A)
EuclideanNorm(x) QuadFormNorm(x,A)
x |
vector or matrix; norm is determined columnwise |
A |
pos. semidefinite Matrix |
the columnwise evaluated norms
Peter Ruckdeschel [email protected]
mm <- matrix(rnorm(20),2,10) EuclideanNorm(mm) QuadFormNorm(mm, A = PosSemDefSymmMatrix(matrix(c(3,1,1,1),2,2)))
mm <- matrix(rnorm(20),2,10) EuclideanNorm(mm) QuadFormNorm(mm, A = PosSemDefSymmMatrix(matrix(c(3,1,1,1),2,2)))
Generates an object of class "L2LocationFamily"
which
represents a normal location family.
NormLocationFamily(mean = 0, sd = 1, trafo)
NormLocationFamily(mean = 0, sd = 1, trafo)
mean |
mean |
sd |
standard deviation |
trafo |
function in |
The slots of the corresponding L2 differentiable parameteric family are filled.
Object of class "L2LocationFamily"
Matthias Kohl [email protected]
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.
L2ParamFamily-class
, Norm-class
(N1 <- NormLocationFamily()) plot(N1) L2derivDistr(N1)
(N1 <- NormLocationFamily()) plot(N1) L2derivDistr(N1)
Generates an object of class "L2LocationScaleFamily"
which
represents a normal location and scale family.
NormLocationScaleFamily(mean = 0, sd = 1, trafo)
NormLocationScaleFamily(mean = 0, sd = 1, trafo)
mean |
mean |
sd |
standard deviation |
trafo |
function in |
The slots of the corresponding L2 differentiable parameteric family are filled.
Object of class "L2LocationScaleFamily"
Matthias Kohl [email protected]
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.
L2ParamFamily-class
, Norm-class
(N1 <- NormLocationScaleFamily()) ## synonymous: N1 <- NormFamily() plot(N1) FisherInfo(N1) checkL2deriv(N1)
(N1 <- NormLocationScaleFamily()) ## synonymous: N1 <- NormFamily() plot(N1) FisherInfo(N1) checkL2deriv(N1)
Generates an object of class "L2LocationScaleFamily"
which
represents a normal location family with unknown scale as nuisance.
NormLocationUnknownScaleFamily(mean = 0, sd = 1, trafo)
NormLocationUnknownScaleFamily(mean = 0, sd = 1, trafo)
mean |
mean |
sd |
standard deviation |
trafo |
function in |
The slots of the corresponding L2 differentiable parameteric family are filled.
Object of class "L2LocationScaleFamily"
Matthias Kohl [email protected]
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.
L2ParamFamily-class
, Norm-class
(N1 <- NormLocationUnknownScaleFamily()) plot(N1) FisherInfo(N1) checkL2deriv(N1)
(N1 <- NormLocationUnknownScaleFamily()) plot(N1) FisherInfo(N1) checkL2deriv(N1)
Generates an object of class "L2ScaleFamily"
which
represents a normal scale family.
NormScaleFamily(sd = 1, mean = 0, trafo)
NormScaleFamily(sd = 1, mean = 0, trafo)
sd |
standard deviation |
mean |
mean |
trafo |
function in |
The slots of the corresponding L2 differentiable parameteric family are filled.
Object of class "L2ScaleFamily"
Matthias Kohl [email protected]
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.
L2ParamFamily-class
, Norm-class
(N1 <- NormScaleFamily()) plot(N1) FisherInfo(N1) checkL2deriv(N1)
(N1 <- NormScaleFamily()) plot(N1) FisherInfo(N1) checkL2deriv(N1)
Generates an object of class "L2LocationScaleFamily"
which
represents a normal scale family with unknown location as nuisance.
NormScaleUnknownLocationFamily(sd = 1, mean = 0, trafo)
NormScaleUnknownLocationFamily(sd = 1, mean = 0, trafo)
mean |
mean |
sd |
standard deviation |
trafo |
function in |
The slots of the corresponding L2 differentiable parameteric family are filled.
Object of class "L2LocationScaleFamily"
Matthias Kohl [email protected]
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.
L2ParamFamily-class
, Norm-class
(N1 <- NormScaleUnknownLocationFamily()) plot(N1) FisherInfo(N1) checkL2deriv(N1)
(N1 <- NormScaleUnknownLocationFamily()) plot(N1) FisherInfo(N1) checkL2deriv(N1)
Generates an object of class "NormType"
.
NormType(name = "EuclideanNorm", fct = EuclideanNorm)
NormType(name = "EuclideanNorm", fct = EuclideanNorm)
name |
slot |
fct |
slot |
Object of class "NormType"
Peter Ruckdeschel [email protected]
Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.
## IGNORE_RDIFF_BEGIN NormType() ## IGNORE_RDIFF_END
## IGNORE_RDIFF_BEGIN NormType() ## IGNORE_RDIFF_END
Class of norm types.
Could be generated by new("NormType")
; more frequently one will use
the generating function NormType
name
Object of class "character"
.
fct
Object of class "function"
— the norm to be evaluated.
signature(object = "NormType")
:
accessor function for slot name
.
signature(object = "NormType", value = "character")
:
replacement function for slot name
.
signature(object = "NormType")
:
accessor function for slot fct
.
signature(object = "NormType", value = "function")
:
replacement function for slot fct
.
Peter Ruckdeschel [email protected]
Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.
## IGNORE_RDIFF_BEGIN EuclNorm <- NormType("EuclideanNorm",EuclideanNorm) fct(EuclNorm) name(EuclNorm) ## IGNORE_RDIFF_END
## IGNORE_RDIFF_BEGIN EuclNorm <- NormType("EuclideanNorm",EuclideanNorm) fct(EuclNorm) name(EuclNorm) ## IGNORE_RDIFF_END
Generates an object of class "OddSymmetric"
.
OddSymmetric(SymmCenter = 0)
OddSymmetric(SymmCenter = 0)
SymmCenter |
numeric: center of symmetry |
Object of class "OddSymmetric"
Matthias Kohl [email protected]
OddSymmetric-class
, FunctionSymmetry-class
OddSymmetric() ## The function is currently defined as function(SymmCenter = 0){ new("OddSymmetric", SymmCenter = SymmCenter) }
OddSymmetric() ## The function is currently defined as function(SymmCenter = 0){ new("OddSymmetric", SymmCenter = SymmCenter) }
Class for odd functions.
Objects can be created by calls of the form new("OddSymmetric")
.
More frequently they are created via the generating function
OddSymmetric
.
type
Object of class "character"
:
contains “odd function”
SymmCenter
Object of class "numeric"
:
center of symmetry
Class "FunctionSymmetry"
, directly.
Class "Symmetry"
, by class "FunctionSymmetry"
.
Matthias Kohl [email protected]
OddSymmetric
, FunctionSymmetry-class
new("OddSymmetric")
new("OddSymmetric")
Class of onesided bias types.
Objects can be created by calls of the form new("onesidedBias", ...)
.
More frequently they are created via the generating function
positiveBias
or negativeBias
.
name
Object of class "character"
.
sign
Object of class "numeric"
;
to be in {-1,1} — whether bias is to be positive or negative
signature(object = "onesidedBias")
:
accessor function for slot sign
.
signature(object = "onesidedBias", value = "numeric")
:
replacement function for slot sign
.
Class "BiasType"
, directly.
Peter Ruckdeschel [email protected]
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.
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
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
Generates an object of class "ParamFamily"
.
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)
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)
name |
character string: name of family |
distribution |
object of class |
distrSymm |
object of class |
startPar |
|
makeOKPar |
|
main |
numeric vector: main parameter |
nuisance |
numeric vector: nuisance parameter |
fixed |
numeric vector: fixed part of the parameter |
trafo |
function in |
param |
object of class |
modifyParam |
function: mapping from the parameter space
(represented by |
props |
character vector: properties of the family |
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) }
.
Object of class "ParamFamily"
Matthias Kohl [email protected],
Peter Ruckdeschel [email protected]
## "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
## "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
Class of parametric families of probability measures.
Objects can be created by calls of the form new("ParamFamily", ...)
.
More frequently they are created via the generating function
ParamFamily
.
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 kStepEstimator
s one
evaluates the asymptotic variance or just produces a call to do so.
Class "ProbFamily"
, directly.
signature(object = "ParamFamily")
:
wrapped accessor function for slot main
of
slot param
.
signature(object = "ParamFamily")
:
wrapped accessor function for slot nuisance
of slot param
.
signature(object = "ParamFamily")
:
wrapped accessor function for slot fixed
of slot param
.
signature(object = "ParamFamily", param = "missing")
:
wrapped accessor function for slot trafo
of slot param
.
signature(object = "ParamFamily")
:
accessor function for slot param
.
signature(object = "ParamFamily")
:
accessor function for slot modifyParam
.
signature(object = "ParamFamily")
:
accessor function for slot fam.call
.
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.
signature(object = "ParamFamily")
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
.
Matthias Kohl [email protected]
F1 <- new("ParamFamily") # prototype plot(F1)
F1 <- new("ParamFamily") # prototype plot(F1)
Generates an object of class "ParamFamParameter"
.
ParamFamParameter(name, main = numeric(0), nuisance, fixed, trafo, ..., .returnClsName = NULL)
ParamFamParameter(name, main = numeric(0), nuisance, fixed, trafo, ..., .returnClsName = NULL)
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.\ |
.returnClsName |
character or |
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.
Object of class "ParamFamParameter"
(or, if non-null, of class
.returnClsName
)
Matthias Kohl [email protected],
Peter Ruckdeschel [email protected]
ParamFamParameter(main = 0, nuisance = 1, fixed = 2, trafo = function(x) list(fval = sin(x), mat = matrix(cos(x),1,1)) )
ParamFamParameter(main = 0, nuisance = 1, fixed = 2, trafo = function(x) list(fval = sin(x), mat = matrix(cos(x),1,1)) )
Class of the parameter of parametric families of probability measures.
Objects can be created by calls of the form new("ParamFamParameter", ...)
.
More frequently they are created via the generating function
ParamFamParameter
.
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?
Class "Parameter"
, directly.
Class "OptionalParameter"
, by class "Parameter"
.
signature(object = "ParamFamParameter")
:
accessor function for slot main
.
signature(object = "ParamFamParameter")
:
replacement function for slot main
.
signature(object = "ParamFamParameter")
:
accessor function for slot nuisance
.
signature(object = "ParamFamParameter")
:
replacement function for slot nuisance
.
signature(object = "ParamFamParameter")
:
accessor function for slot fixed
.
signature(object = "ParamFamParameter")
:
replacement function for slot fixed
.
signature(object = "ParamFamParameter")
:
accessor function for slot trafo
.
signature(object = "ParamFamParameter")
:
replacement function for slot trafo
.
signature(x = "ParamFamParameter")
:
sum of the lengths of main
and nuisance
.
signature(x = "ParamFamParameter")
:
length of main
.
signature(object = "ParamWithShapeFamParameter")
:
accessor function for slot trafo
.
signature(object = "ParamWithShapeFamParameter")
:
replacement function for slot trafo
.
signature(object = "ParamFamParameter")
signature(object = "ParamWithShapeFamParameter")
signature(object = "ParamWithScaleAndShapeFamParameter")
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.
Matthias Kohl [email protected],
Peter Ruckdeschel [email protected]
new("ParamFamParameter")
new("ParamFamParameter")
Generates an object of class "L2ParamFamily"
which
represents a Poisson family.
PoisFamily(lambda = 1, trafo)
PoisFamily(lambda = 1, trafo)
lambda |
positive mean |
trafo |
function in |
The slots of the corresponding L2 differentiable parameteric family are filled.
Object of class "L2ParamFamily"
Matthias Kohl [email protected]
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.
L2ParamFamily-class
, Pois-class
(P1 <- PoisFamily(lambda = 4.5)) plot(P1) FisherInfo(P1) checkL2deriv(P1)
(P1 <- PoisFamily(lambda = 4.5)) plot(P1) FisherInfo(P1) checkL2deriv(P1)
Generates an object of class "onesidedBias"
.
positiveBias(name = "positive Bias")
positiveBias(name = "positive Bias")
name |
name of the bias type |
Object of class "onesidedBias"
Peter Ruckdeschel [email protected]
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.
positiveBias() ## The function is currently defined as function(){ new("onesidedBias", name = "positive Bias", sign = 1) }
positiveBias() ## The function is currently defined as function(){ new("onesidedBias", name = "positive Bias", sign = 1) }
Methods for print
to the S4 classes in package distrMod;
## S4 method for signature 'ShowDetails' print(x, digits = getOption("digits"), show.details = c("maximal", "minimal", "medium"))
## S4 method for signature 'ShowDetails' print(x, digits = getOption("digits"), show.details = c("maximal", "minimal", "medium"))
x |
object of class |
digits |
unchanged w.r.t. default method of package |
show.details |
a character, controlling the degree of detailedness
of the output; currently the following values are permitted:
|
This method provides sort of a ”show
with extra arguments”, in form of a common print
method
for the mentioned S4 classes. Essentially this print
method
just temporarily sets the global options according to the optional arguments
digits
and show.details
, calls show
and then re-sets
the options to their global settings.
## set options to maximal detailedness show.old <- getdistrModOption("show.details") distrModoptions("show.details" = "maximal") ## define a model 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)) } print(param(NS)) print(param(NS), show.details = "minimal") print(param(NS), show.details = "medium") ## Maximum likelihood estimator res <- MLEstimator(x = x, ParamFamily = NS) print(res) #equivalent to 'show(res)' or 'res' print(res, digits = 4) print(res, show.details = "minimal") print(res, show.details = "medium") distrModoptions("show.details" = show.old)
## set options to maximal detailedness show.old <- getdistrModOption("show.details") distrModoptions("show.details" = "maximal") ## define a model 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)) } print(param(NS)) print(param(NS), show.details = "minimal") print(param(NS), show.details = "medium") ## Maximum likelihood estimator res <- MLEstimator(x = x, ParamFamily = NS) print(res) #equivalent to 'show(res)' or 'res' print(res, digits = 4) print(res, show.details = "minimal") print(res, show.details = "medium") distrModoptions("show.details" = show.old)
Class of families of probability measures.
A virtual Class: No objects may be created from it.
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.
signature(object = "ProbFamily")
:
accessor function for slot name
.
signature(object = "ProbFamily")
:
replacement function for slot name
.
signature(object = "ProbFamily")
:
accessor function for slot distribution
.
signature(object = "ProbFamily")
:
accessor function for slot distrSymm
.
signature(object = "ProbFamily")
:
accessor function for slot props
.
signature(object = "ProbFamily")
:
replacement function for slot props
.
signature(object = "ProbFamily")
:
add a property to slot props
.
signature(object = "ProbFamily")
: wrapped accessor
to slot r
of slot "Distribution"
.
signature(object = "ProbFamily")
: wrapped accessor
to slot d
of slot "Distribution"
.
signature(object = "ProbFamily")
: wrapped accessor
to slot p
of slot "Distribution"
.
signature(object = "ProbFamily")
: wrapped accessor
to slot q
of slot "Distribution"
.
signature(object = "ProbFamily")
: wrapped accessor
to slot q
of slot "Distribution"
– for compatibility
with RStudio or Jupyter IRKernel / synonymous to q
.
Matthias Kohl [email protected]
Generates an object of class "QFNorm"
.
QFNorm(name = "norm based on quadratic form", QuadForm = PosSemDefSymmMatrix(matrix(1)))
QFNorm(name = "norm based on quadratic form", QuadForm = PosSemDefSymmMatrix(matrix(1)))
name |
slot |
QuadForm |
slot |
Object of class "QFNorm"
Peter Ruckdeschel [email protected]
Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.
## IGNORE_RDIFF_BEGIN QFNorm() ## The function is currently defined as function(){ new("QFNorm") } ## IGNORE_RDIFF_END
## IGNORE_RDIFF_BEGIN QFNorm() ## The function is currently defined as function(){ new("QFNorm") } ## IGNORE_RDIFF_END
Classes for norms based on quadratic forms
could be created by a call to new
, but
normally one would use the generating functions QFNorm
,
InfoNorm
, and SelfNorm
name
Object of class "character"
.
fct
Object of class "function"
.
QuadForm
Object of class "PosSemDefSymmMatrix"
.
"QFNorm"
extends class "NormType"
, directly,
and "InfoNorm"
and "SelfNorm"
each extend
class "QFNorm"
, directly (and do not have extra slots).
signature(object = "QFNorm")
:
accessor function for slot QuadForm
.
signature(object = "QFNorm")
:
replacement function for slot QuadForm
.
Peter Ruckdeschel [email protected]
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.
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
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$double.eps, check.NotInSupport = TRUE, col.NotInSupport = "red", with.legend = TRUE, legend.bg = "white", legend.pos = "topleft", legend.cex = 0.8, legend.pref = "", legend.postf = "", legend.alpha = alpha.CI, debug = FALSE, withSubst = TRUE) ## S4 method for signature 'ANY,ProbFamily' qqplot(x, y, n = length(x), withIdLine = TRUE, withConf = TRUE, withConf.pw = withConf, withConf.sim = withConf, plot.it = TRUE, xlab = deparse(substitute(x)), ylab = deparse(substitute(y)), ...) ## S4 method for signature 'ANY,Estimate' qqplot(x, y, n = length(x), withIdLine = TRUE, withConf = TRUE, withConf.pw = withConf, withConf.sim = withConf, plot.it = TRUE, xlab = deparse(substitute(x)), ylab = deparse(substitute(y)), ...)
qqplot(x, y, ...) ## S4 method for signature 'ANY,UnivariateDistribution' qqplot(x,y, n = length(x), withIdLine = TRUE, withConf = TRUE, withConf.pw = withConf, withConf.sim = withConf, plot.it = TRUE, datax = FALSE, xlab = deparse(substitute(x)), ylab = deparse(substitute(y)), ..., width = 10, height = 5.5, withSweave = getdistrOption("withSweave"), mfColRow = TRUE, n.CI = n, with.lab = FALSE, lab.pts = NULL, which.lbs = NULL, which.Order = NULL, which.nonlbs = NULL, attr.pre = FALSE, order.traf = NULL, col.IdL = "red", lty.IdL = 2, lwd.IdL = 2, alpha.CI = .95, exact.pCI = (n<100), exact.sCI = (n<100), nosym.pCI = FALSE, col.pCI = "orange", lty.pCI = 3, lwd.pCI = 2, pch.pCI = par("pch"), cex.pCI = par("cex"), col.sCI = "tomato2", lty.sCI = 4, lwd.sCI = 2, pch.sCI = par("pch"), cex.sCI = par("cex"), added.points.CI = TRUE, cex.pch = par("cex"), col.pch = par("col"), cex.pts = 1, col.pts = par("col"), pch.pts = 19, cex.npts = 1, col.npts = grey(.5), pch.npts = 20, cex.lbs = par("cex"), col.lbs = par("col"), adj.lbs = par("adj"), alpha.trsp = NA, jit.fac = 0, jit.tol = .Machine$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)), ...)
x |
data to be checked for compatibility with distribution/model |
y |
object of class |
n |
numeric; assumed sample size (by default length of |
withIdLine |
logical; shall line |
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
|
datax |
logical; shall data be plotted on x-axis? |
xlab |
x-label |
ylab |
y-label |
... |
further parameters for method |
width |
width (in inches) of the graphics device opened |
height |
height (in inches) of the graphics device opened |
withSweave |
logical: if |
mfColRow |
shall default partition in panels be used — defaults to |
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 |
attr.pre |
logical; do graphical attributes for plotted data refer
to indices prior ( |
which.lbs |
integer or |
which.Order |
integer or |
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 |
order.traf |
function or |
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.pch |
color for the plotted symbols (for backward compatibility); it is
ignored once |
cex.pts |
size of the points of the second argument plotted, can be a vector;
if argument |
col.pts |
color of the points of the second argument plotted, can
be a vector as in |
pch.pts |
symbol of the points of the second argument plotted, can
be a vector as in |
col.npts |
color of the non-labelled points of the |
pch.npts |
symbol of the non-labelled points of the |
cex.npts |
size of the non-labelled points of the |
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
|
jit.fac |
jittering factor used for discrete distributions. |
jit.tol |
threshold for jittering: if distance between points is smaller
than |
check.NotInSupport |
logical; shall we check if all |
col.NotInSupport |
logical; if preceding check |
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 |
withSubst |
logical; if |
signature(x = "ANY", y = "UnivariateDistribution")
:
produces a QQ plot of a dataset x
against the theoretical
quantiles of distribution y
.
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.
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.
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 |
crit |
A matrix with the lower and upper confidence bounds
(computed by |
err |
logical vector of length 2. |
(elements crit
and err
are taken from the return
value(s) of qqbounds
).
Peter Ruckdeschel [email protected]
Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole.
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.
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)
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)
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
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$double.eps, check.NotInSupport = TRUE, col.NotInSupport = "red", with.legend = TRUE, legend.bg = "white", legend.pos = "topleft", legend.cex = 0.8, legend.pref = "", legend.postf = "", legend.alpha = alpha.CI, debug = FALSE, withSubst = TRUE) ## S4 method for signature 'ANY,ProbFamily' returnlevelplot(x, y, n = length(x), withIdLine = TRUE, withConf = TRUE, withConf.pw = withConf, withConf.sim = withConf, plot.it = TRUE, xlab = deparse(substitute(x)), ylab = deparse(substitute(y)), ...) ## S4 method for signature 'ANY,Estimate' returnlevelplot(x, y, n = length(x), withIdLine = TRUE, withConf = TRUE, withConf.pw = withConf, withConf.sim = withConf, plot.it = TRUE, xlab = deparse(substitute(x)), ylab = deparse(substitute(y)), ...)
returnlevelplot(x, y, ...) ## S4 method for signature 'ANY,UnivariateDistribution' returnlevelplot(x,y, n = length(x), withIdLine = TRUE, withConf = TRUE, withConf.pw = withConf, withConf.sim = withConf, plot.it = TRUE, datax = FALSE, MaxOrPOT = c("Max","POT"), npy = 365, threshold = if(is(y,"GPareto")) NA else 0, xlab = deparse(substitute(x)), ylab = deparse(substitute(y)), main = "", ..., width = 10, height = 5.5, withSweave = getdistrOption("withSweave"), mfColRow = TRUE, n.CI = n, with.lab = FALSE, lab.pts = NULL, which.lbs = NULL, which.Order = NULL, which.nonlbs = NULL, attr.pre = FALSE, order.traf = NULL, col.IdL = "red", lty.IdL = 2, lwd.IdL = 2, alpha.CI = .95, exact.pCI = (n<100), exact.sCI = (n<100), nosym.pCI = FALSE, col.pCI = "orange", lty.pCI = 3, lwd.pCI = 2, pch.pCI = par("pch"), cex.pCI = par("cex"), col.sCI = "tomato2", lty.sCI = 4, lwd.sCI = 2, pch.sCI = par("pch"), cex.sCI = par("cex"), added.points.CI = TRUE, cex.pch = par("cex"), col.pch = par("col"), cex.pts = 1, col.pts = par("col"), pch.pts = 19, cex.npts = 1, col.npts = grey(.5), pch.npts = 20, cex.lbs = par("cex"), col.lbs = par("col"), adj.lbs = par("adj"), alpha.trsp = NA, jit.fac = 0, jit.tol = .Machine$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)), ...)
x |
data to be checked for compatibility with distribution/model |
y |
object of class |
n |
numeric; assumed sample size (by default length of |
withIdLine |
logical; shall line |
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
|
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 |
main |
Main title |
xlab |
x-label |
ylab |
y-label |
... |
further parameters for method |
width |
width (in inches) of the graphics device opened |
height |
height (in inches) of the graphics device opened |
withSweave |
logical: if |
mfColRow |
shall default partition in panels be used — defaults to |
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 |
attr.pre |
logical; do graphical attributes for plotted data refer
to indices prior ( |
which.lbs |
integer or |
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 |
which.Order |
integer or |
order.traf |
function or |
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.pch |
color for the plotted symbols (for backward compatibility); it is
ignored once |
cex.pts |
size of the points of the second argument plotted, can be a vector;
if argument |
col.pts |
color of the points of the second argument plotted, can
be a vector as in |
pch.pts |
symbol of the points of the second argument plotted, can
be a vector as in |
col.npts |
color of the non-labelled points of the |
pch.npts |
symbol of the non-labelled points of the |
cex.npts |
size of the non-labelled points of the |
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
|
jit.fac |
jittering factor used for discrete distributions. |
jit.tol |
threshold for jittering: if distance between points is smaller
than |
check.NotInSupport |
logical; shall we check if all |
col.NotInSupport |
logical; if preceding check |
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 |
withSubst |
logical; if |
signature(x = "ANY", y = "UnivariateDistribution")
:
produces a return level plot of a dataset x
against the theoretical
quantiles of distribution y
.
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.
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.
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 |
crit |
A matrix with the lower and upper confidence bounds
(computed by |
err |
logical vector of length 2. |
(elements crit
and err
are taken from the return
value(s) of qqbounds
).
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.
Peter Ruckdeschel [email protected]
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.
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.
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$mle[2],loc=10) returnlevelplot(rain, GPDF, MaxOrPOT="POT", xlim=c(1e-1,1e3)) } ## IGNORE_RDIFF_END
set.seed(20190331) returnlevelplot(r(Norm(15,sqrt(30)))(40), Chisq(df=15)) ### more could be seen after installing RobExtremes and ismev # ## IGNORE_RDIFF_BEGIN ## at R CMD check --as-cran, it does not find package cluster ## when trying to attach package rrcov ## so remove this from testing if(require(RobExtremes) && require(ismev)){ data(portpirie) gevfit <- gev.fit(portpirie[,2]) ## taken from example from ismev::gev.fit GEVF <- GEVFamily(scale=gevfit$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
Class of risks; e.g., estimator risks.
A virtual Class: No objects may be created from it.
type
Object of class "character"
:
type of risk.
signature(object = "RiskType")
:
accessor function for slot type
.
signature(object = "RiskType")
Matthias Kohl [email protected]
Generates an object of class "SelfNorm"
—
used for self-standardized influence curves.
SelfNorm()
SelfNorm()
Object of class "SelfNorm"
Matthias Kohl [email protected]
Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.
## IGNORE_RDIFF_BEGIN SelfNorm() ## The function is currently defined as function(){ new("SelfNorm") } ## IGNORE_RDIFF_END
## IGNORE_RDIFF_BEGIN SelfNorm() ## The function is currently defined as function(){ new("SelfNorm") } ## IGNORE_RDIFF_END
Generates an object of class "symmetricBias"
.
symmetricBias(name = "symmetric Bias")
symmetricBias(name = "symmetric Bias")
name |
name of the bias type |
Object of class "symmetricBias"
Peter Ruckdeschel [email protected]
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.
symmetricBias() ## The function is currently defined as function(){ new("symmetricBias", name = "symmetric Bias") }
symmetricBias() ## The function is currently defined as function(){ new("symmetricBias", name = "symmetric Bias") }
Class of symmetric bias types.
Objects can be created by calls of the form new("symmetricBias", ...)
.
More frequently they are created via the generating function
symmetricBias
.
name
Object of class "character"
.
No methods defined with class "symmetricBias" in the signature.
Class "BiasType"
, directly.
Peter Ruckdeschel [email protected]
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.
symmetricBias() ## The function is currently defined as function(){ new("symmetricBias", name = "symmetric Bias") }
symmetricBias() ## The function is currently defined as function(){ new("symmetricBias", name = "symmetric Bias") }
Methods for function trafo
in package distrMod;
there are accessor (trafo
) and replacement (trafo<-
)
versions.
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
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
object |
an object of either class |
param |
an object of class |
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 |
... |
additional argument(s) for methods; not used so far. |
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:
Estimate,missing
:returns a list of length two with components
fct
and mat
(see below)
Estimate,ParamFamParameter
:returns a list of length two with components
fct
and mat
(see below)
ParamFamParameter,missing
:returns a matrix (see below)
ParamFamily,missing
:returns a matrix (see below)
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
of the parameter
.
For the this function , 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 is split up coordinate-wise
in a main parameter
and a nuisance parameter
(which is unknown, too, hence has to be
estimated, but only is of secondary interest) and a fixed,
known part
.
Without loss of generality, we restrict ourselves to the case that
transformation only acts on the main parameter
— if we want to transform the whole
parameter, we only have to assume that both nuisance parameter
and fixed, known part of the parameter
have length 0.
To the implementation:
Slot trafo
can either contain a (constant) matrix
or a function
mapping main parameter
to some range
.
If slot value trafo
is a function, besides ,
it will also return the corresponding derivative matrix
.
More specifically, the return value of this function
theta
is a
list with entries fval
, the function value ,
and
mat
, the derivative matrix.
In case trafo
is a matrix , we interpret it as such a derivative
matrix
,
and, correspondingly,
as the linear mapping
.
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 , and
mat
, the matrix
.
function
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
.
## 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)
## 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)
trafoEst
takes a like function (compare
trafo-methods
) and transforms an existing estimator by means
of this transformation.
trafoEst(fct, estimator)
trafoEst(fct, estimator)
fct |
a |
estimator |
an object of class |
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.
exactly the argument estimator
, but with modified slots
estimate
, asvar
, and trafo
.
## 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)
## 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)
Generates an object of class "trAsCov"
.
trAsCov()
trAsCov()
Object of class "trAsCov"
Matthias Kohl [email protected]
Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.
trAsCov() ## The function is currently defined as function(){ new("trAsCov") }
trAsCov() ## The function is currently defined as function(){ new("trAsCov") }
Class of trace of asymptotic covariance.
Objects can be created by calls of the form new("trAsCov", ...)
.
More frequently they are created via the generating function
trAsCov
.
type
Object of class "character"
:
“trace of asymptotic covariance”.
Class "asRisk"
, directly.
Class "RiskType"
, by class "asRisk"
.
Matthias Kohl [email protected]
Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.
new("trAsCov")
new("trAsCov")
Generates an object of class "trFiCov"
.
trFiCov()
trFiCov()
Object of class "trFiCov"
Matthias Kohl [email protected]
Ruckdeschel, P. and Kohl, M. (2005) How to approximate the finite sample risk of M-estimators.
trFiCov() ## The function is currently defined as function(){ new("trFiCov") }
trFiCov() ## The function is currently defined as function(){ new("trFiCov") }
Class of trace of finite-sample covariance.
Objects can be created by calls of the form new("trFiCov", ...)
.
More frequently they are created via the generating function
trFiCov
.
type
Object of class "character"
:
“trace of finite-sample covariance”.
Class "fiRisk"
, directly.
Class "RiskType"
, by class "fiRisk"
.
Matthias Kohl [email protected]
Ruckdeschel, P. and Kohl, M. (2005) How to approximate the finite sample risk of M-estimators.
new("trFiCov")
new("trFiCov")
Methods for function validParameter
in package distrMod
to check whether a new parameter (e.g. "proposed" by an optimization)
is valid.
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)
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)
object |
an object of class |
param |
either a numeric vector or an object of class
|
tol |
accuracy upto which the conditions have to be fulfilled |
... |
additional argument(s) for methods. |
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
)
logical
of length 1 — valid or not
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))
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))