Package 'RobAStBase'

Description

Base S4-classes and functions for robust asymptotic statistics.

Details

Package versions

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

Author(s)

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

References

M. Kohl (2005). Numerical Contributions to the Asymptotic Theory of Robustness. Dissertation. University of Bayreuth. See also https://www.stamats.de/wp-content/uploads/2018/04/ThesisMKohl.pdf

See Also

distr-package, distrEx-package, distrMod-package

Examples

library(RobAStBase)
## some L2 differentiable parametric family from package distrMod, e.g.
B <- BinomFamily(size = 25, prob = 0.25) 
## classical optimal IC
IC0 <- optIC(model = B, risk = asCov())
plot(IC0) # plot IC
checkIC(IC0, B)

Description

Class of asymptotically linear estimates.

Details

The (return value) class of an estimator is of class ALEstimate if it is asymptotically linear; then it has an influence function (implemented in slot pIC) and so all the diagnostics for influence functions are available; in addition it is asymptotically normal, so we can (easily) deduce asymptotic covariances, hence may use these in confidence intervals; in particular, the return values of kStepEstimator oneStepEstimator (and roptest, robest, RMXEstimator, MBREstimator, OBREstimator, OMSEstimator in package 'ROptEst') are objects of (subclasses of) this class.

As the return value of CvMMDEEstimator (or MDEstimator with CvMDist or CvMDist2 as distance) is asymptotically linear, there is class MCALEstimate extending MCEstimate by extra slots pIC and asbias (only filled optionally with non-NULL values). Again all the diagnostics for influence functions are then available. Classes ML.ALEstimate and class CvMMD.ALEstimate are nominal subclasses of class MCALEstimate, nominal in the sense that they have no extra slots, but they might have particular methods later on.

Helper method getPIC by means of the estimator class, and, in case of estimators of class CvMMDEstimate, also the name (in slot name) produces the (partial) influence function: calling .CvMMDCovariance – either directly or through wrapper .CvMMDCovarianceWithMux. This is used in the corresponding .checkEstClassForParamFamily method, which coerces object from class "MCEstimate" to "MCALEstimate".

Objects from the Class

Objects can be created by calls of the form new("ALEstimate", ...).

Slots

name

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

estimate

Object of class "ANY": estimate.

estimate.call

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

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.

asvar

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

asbias

Optional object of class "numeric": asymptotic bias.

pIC

Optional object of class InfluenceCurve: influence curve.

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

Infos

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

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.

Extends

Class ALEstimate extends class "Estimate", directly. Class MCALEstimate extends classes "ALEstimate", and "MCEstimate" directly. Class ML.ALEstimate extends classes "ALEstimate", and "MLEstimate" directly. Class CvM.ALEstimate extends classes "ALEstimate", and "CvMMDEstimate" directly. The last two classes are to be used for method dispatch, later; they have an identical slot structure to class MCALEstimate.

Methods

pIC

signature(object = "ALEstimate"): accessor function for slot pIC.

show

signature(object = "ALEstimate")

confint

signature(object = "ALEstimate", method = "missing"): compute asymptotic (LAN-based) confidence interval neglecting any bias.

confint

signature(object = "ALEstimate", method = "symmetricBias"): compute asymptotic (LAN-based) confidence interval incorporating bias symmetrically.

confint

signature(object = "ALEstimate", method = "onesidedBias"): compute asymptotic (LAN-based) confidence interval incorporating bias one-sided; i.e., positive or negative, respectively.

confint

signature(object = "ALEstimate", method = "asymmetricBias"): compute asymptotic (LAN-based) confidence interval incorporating bias asymmetrically.

Author(s)

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

See Also

Estimate-class

Examples

## prototype
new("ALEstimate")

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

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

mle <- MLEstimator(x,G)
(picM <- pIC(mle))

## Kolmogorov(-Smirnov) minimum distance estimator
ke <- KolmogorovMDEstimator(x = x, ParamFamily = G)
pIC(ke) ## gives NULL

## von Mises minimum distance estimator with default mu

 ## to save time for CRAN
system.time(me <- CvMMDEstimator(x = x, ParamFamily = G))
str(me@pIC) ## a call
system.time(pIC0 <- pIC(me))
str(me@pIC) ## now filled

Description

Classes for bounded, robust, standardized weights.

Objects from the Class

Objects can be created by calls of the form new("BdStWeight", ...); to fill slot weight, you will use the generating functions getweight and minbiasweight.

Slots

name

Object of class "character"; inherited from class RobWeight.

weight

Object of class "function" — the weight function; inherited from class RobWeight.

clip

Object of class "numeric" — clipping bound(s); inherited from class BoundedWeight.

stand

Object of class "matrix" — standardization.

Extends

Class "RobWeight", via class "BoundedWeight". Class "BoundedWeight", directly.

Methods

stand

signature(object = "BdStWeight"): accessor function for slot stand.

stand<-

signature(object = "BdStWeight", value = "matrix"): replacement function for slot stand. This replacement method should be used with great care, as the slot weight is not simultaneously updated and hence, this may lead to inconsistent objects.

Author(s)

Peter Ruckdeschel [email protected]

References

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

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

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

See Also

BoundedWeight-class, RobWeight-class, IC, InfluenceCurve-class

Examples

## prototype
new("BdStWeight")

Description

biastype-methods

Methods

biastype

signature(object = "interpolrisk"): returns the slot biastype of an object of class "interpolrisk".

Examples

myrisk <- MBRRisk(samplesize=100)
biastype(myrisk)

Description

Classes for bounded, robust weights.

Objects from the Class

Objects can be created by calls of the form new("BoundedWeight", ...).

Slots

name

Object of class "character"; inherited from class RobWeight.

weight

Object of class "function" — the weight function; inherited from class RobWeight.

clip

Object of class "numeric" — clipping bound(s).

Extends

Class "RobWeight", directly.

Methods

clip

signature(x1 = "BoundedWeight"): accessor function for slot clip.

clip<-

signature(object = "BoundedWeight", value = "numeric"): replacement function for slot clip. This replacement method should be used with great care, as the slot weight is not simultaneously updated and hence, this may lead to inconsistent objects.

Author(s)

Peter Ruckdeschel [email protected]

References

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

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

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

See Also

RobWeight-class, IC, InfluenceCurve-class

Examples

## prototype
new("BoundedWeight")

Description

Generic function for checking centering and Fisher consistency of ICs.

Usage

checkIC(IC, L2Fam, ...)
## S4 method for signature 'IC,missing'
checkIC(IC, out = TRUE, ..., diagnostic = FALSE)
## S4 method for signature 'IC,L2ParamFamily'
checkIC(IC, L2Fam, out = TRUE,..., diagnostic = FALSE)

Arguments

Details

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

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.

Value

The maximum deviation from the IC properties is returned.

Author(s)

Matthias Kohl [email protected]

References

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

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

See Also

L2ParamFamily-class, IC-class

Examples

IC1 <- new("IC")
checkIC(IC1)

Description

The wrapper ComparePlot (capital C!) takes most of arguments to function comparePlot (lower case c!) by default and gives a user possibility to run the function with low number of arguments.

Usage

ComparePlot(IC1, IC2,  y, ..., IC3 = NULL, IC4 = NULL,
    alpha.trsp = 100, with.legend = TRUE, rescale = FALSE,
    withCall = TRUE)

Arguments

Value

invisible(retV) where retV is the return value of the respective call to the full-fledged function comparePlot with the additional item wrapcall with the call to the wrapper ComparePlot and wrappedcall the call to to the full-fledged function comparePlot.

Details

Calls comparePlot with suitably chosen defaults; if withCall == TRUE, the call to comparePlot, i.e., item wrappedcall of the (hidden) return value, is printed.

Examples

# Gamma
fam <- GammaFamily()
rfam <- InfRobModel(fam, ContNeighborhood(0.5))
IC1 <- optIC(model = fam, risk = asCov())
IC2 <- makeIC(list(function(x)sin(x),function(x)x^2), L2Fam = fam)
Y <- distribution(fam)
y <- r(Y)(100)
ComparePlot(IC1, IC2, y, withCall = TRUE)

Description

Plots 2-4 influence curves to the same model.

Usage

comparePlot(obj1, obj2, ... )
## S4 method for signature 'IC,IC'
comparePlot(obj1, obj2, obj3 = NULL, obj4 = NULL, data = NULL,
                 ..., withSweave = getdistrOption("withSweave"),
                 forceSameModel = FALSE, main = FALSE, inner = TRUE,
                 sub = FALSE, col = par("col"), lwd = par("lwd"), lty,
                 col.inner = par("col.main"), cex.inner = 0.8,
                 bmar = par("mar")[1], tmar = par("mar")[3],
                 with.automatic.grid = TRUE, with.legend = FALSE,
                 legend = NULL, legend.bg = "white",
                 legend.location = "bottomright", legend.cex = 0.8,
                 withMBR = FALSE, MBRB = NA, MBR.fac = 2, col.MBR = par("col"),
                 lty.MBR = "dashed", lwd.MBR = 0.8, x.vec = NULL,
                 scaleX = FALSE, scaleX.fct, scaleX.inv, scaleY = FALSE,
                 scaleY.fct = pnorm, scaleY.inv = qnorm, scaleN = 9,
                 x.ticks = NULL, y.ticks = NULL, mfColRow = TRUE,
                 to.draw.arg = NULL,
                 cex.pts = 1, cex.pts.fun = NULL, col.pts = par("col"),
                 pch.pts = 19, cex.npts = 1, cex.npts.fun = NULL,
                 col.npts = par("col"), pch.npts = 20, jitter.fac = 1,
                 with.lab = FALSE, cex.lbs = 1, adj.lbs = c(0, 0),
                 col.lbs = col.pts, lab.pts = NULL, lab.font = NULL,
                 alpha.trsp = NA, which.lbs = NULL, which.Order = NULL,
                 which.nonlbs = NULL, attr.pre = FALSE, return.Order = FALSE,
                 withSubst = TRUE)

Arguments

Details

Any parameters of plot.default may be passed on to this particular plot method.

For main-, inner, and subtitles given as arguments main, inner, and sub, top and bottom margins are enlarged to 5 resp. 6 by default but may also be specified by tmar / bmar arguments. If main / inner / sub are logical then if the respective argument is FALSE nothing is done/plotted, but if it is TRUE, we use a default main title taking up the calling arguments in case of main, default inner titles taking up the class and (named) parameter slots of arguments in case of inner, and a "generated on <data>"-tag in case of sub. Of course, if main / inner / sub are character, this is used for the title; in case of inner it is then checked whether it has correct length. If argument withSubst is TRUE, in all title and axis lable arguments, the following patterns are substituted:

"%C1","%C2",["%C3",]["%C4"]

class of argument obj<i>, i=1,..4

"%A1","%A2",["%A3",]["%A4"]

deparsed argument obj<i>, i=1,..4

"%D"

time/date-string when the plot was generated

If argument ... contains argument ylim, this may either be as in plot.default (i.e. a vector of length 2) or a vector of length 2*(number of plotted dimensions); in the case of longer length, these are the values for ylim for the plotted dimensions of the IC, one pair for each dimension.

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).

Value

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.

Author(s)

Peter Ruckdeschel [email protected]

References

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

See Also

L2ParamFamily-class, IC-class, plot

Examples

if(require(ROptEst)){

N0 <- NormLocationScaleFamily(mean=0, sd=1) 
N0.Rob1 <- InfRobModel(center = N0, neighbor = ContNeighborhood(radius = 0.5))

IC1 <- optIC(model = N0, risk = asCov())
IC2 <- optIC(model = N0.Rob1, risk = asMSE())

comparePlot(IC1,IC2)

set.seed(12); data <- r(N0)(20)
comparePlot(IC1, IC2, data=data, with.lab = TRUE,
            which.lbs = c(1:4,15:20),
            which.Order = 1:6,
            return.Order = TRUE)


## don't test to reduce check time on CRAN

## selection of subpanels for plotting
par(mfrow=c(1,1))
comparePlot(IC1, IC2 ,mfColRow = FALSE, to.draw.arg=c("mean"),
            panel.first= grid(),ylim=c(-4,4),xlim=c(-6,6))
## matrix-valued ylim
comparePlot(IC1, IC2, panel.first= grid(),ylim=c(-4,4,0,4),xlim=c(-6,6))

x <- c(data,-12,10)
comparePlot(IC1, IC2, data=x, which.Order=10,
            panel.first= grid(), ylim=c(-4,4,0,4), xlim=c(-6,6))

Y <- Chisq(df=1)* DiscreteDistribution(c(-1,1))
comparePlot(IC1, IC2, data=x, which.Order=10,
            scaleX = TRUE, scaleX.fct=pnorm, scaleX.inv=qnorm,
            scaleY = TRUE, scaleY.fct=p(Y), scaleY.inv=q.l(Y),
            panel.first= grid(), ylim=c(-4,4,0,4), xlim=c(-6,6))
comparePlot(IC1, IC2, data=x, which.Order=10,
            scaleX = TRUE, scaleX.fct=pnorm, scaleX.inv=qnorm,
            scaleY = TRUE, scaleY.fct=p(Y), scaleY.inv=q.l(Y),
            x.ticks = c(-Inf, -10, -1,0,1,10,Inf),
            y.ticks = c(-Inf, -5, -1,0,1,5,Inf),
            panel.first= grid(), ylim=c(-4,4,0,4), xlim=c(-6,6))

## with use of trafo-matrix:
G <- GammaFamily(scale = 1, shape = 2)
## 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
G2
G2.Rob1 <- InfRobModel(center = G2, neighbor = ContNeighborhood(radius = 0.5))
system.time(IC1 <- optIC(model = G2, risk = asCov()))
system.time(IC2 <- optIC(model = G2.Rob1, risk = asMSE()))
system.time(IC2.i <- optIC(model = G2.Rob1, risk = asMSE(normtype=InfoNorm())))
system.time(IC2.s <- optIC(model = G2.Rob1, risk = asMSE(normtype=SelfNorm())))

comparePlot(IC1,IC2, IC2.i, IC2.s)


}

Description

Generates an object of class "ContIC"; i.e., an influence curves $\eta$ of the form

$\eta = (A\Lambda - a)\min(1,b/|A\Lambda - a|)$

with clipping bound $b$, centering constant $a$ and standardizing matrix $A$. $\Lambda$ stands for the L2 derivative of the corresponding L2 differentiable parametric family which can be created via CallL2Fam.

Usage

ContIC(name, CallL2Fam = call("L2ParamFamily"), 
       Curve = EuclRandVarList(RealRandVariable(Map = c(function(x){x}), 
                                                Domain = Reals())), 
       Risks, Infos, clip = Inf, cent = 0, stand = as.matrix(1), 
       lowerCase = NULL, neighborRadius = 0, w = new("HampelWeight"),
       normtype = NormType(), biastype = symmetricBias(),
       modifyIC = NULL)

Arguments

Value

Object of class "ContIC"

Author(s)

Matthias Kohl [email protected]

References

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

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

See Also

IC-class, ContIC , HampIC-class

Examples

IC1 <- ContIC()
plot(IC1)

Description

Class of (partial) influence curves of contamination type; i.e., influence curves $\eta$ of the form

$\eta = (A\Lambda - a)\min(1,b/|A\Lambda - a|)$

with clipping bound $b$, centering constant $a$ and standardizing matrix $A$. $\Lambda$ stands for the L2 derivative of the corresponding L2 differentiable parametric family created via the call in the slot CallL2Fam.

Objects from the Class

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

Slots

CallL2Fam:

object of class "call": creates an object of the underlying L2-differentiable parametric family.

name:

object of class "character"

Curve:

object of class "EuclRandVarList"

modifyIC

object of class "OptionalFunction": function of four arguments: (1) L2Fam an L2 parametric family (2) IC an optional influence curve, (3) withMakeIC a logical argument whether to enforce the IC side conditions by makeIC, and (4) ... for arguments to be passed to calls to E in makeIC. Returns an object of class "IC". This function is mainly used for internal computations!

Risks:

object of class "list": list of risks; cf. RiskType-class.

Infos:

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

clip:

object of class "numeric": clipping bound.

cent:

object of class "numeric": centering constant.

stand:

object of class "matrix": standardizing matrix.

weight:

object of class "HampelWeight": weight function

biastype:

object of class "BiasType": bias type (symmetric/onsided/asymmetric)

normtype:

object of class "NormType": norm type (Euclidean, information/self-standardized)

lowerCase:

object of class "OptionalNumeric": optional constant for lower case solution.

neighborRadius:

object of class "numeric": radius of the corresponding (unconditional) contamination neighborhood.

Extends

Class "HampIC", directly.
Class "IC", by class "HampIC".
Class "InfluenceCurve", by class "IC".

Methods

CallL2Fam<-

signature(object = "ContIC"): replacement function for slot CallL2Fam.

cent

signature(object = "ContIC"): accessor function for slot cent.

cent<-

signature(object = "ContIC"): replacement function for slot cent.

clip

signature(x1 = "ContIC"): accessor function for slot clip.

clip<-

signature(object = "ContIC"): replacement function for slot clip.

stand<-

signature(object = "ContIC"): replacement function for slot stand.

lowerCase<-

signature(object = "ContIC"): replacement function for slot lowerCase.

neighbor

signature(object = "ContIC"): generates an object of class "ContNeighborhood" with radius given in slot neighborRadius.

generateIC

signature(neighbor = "ContNeighborhood", L2Fam = "L2ParamFamily"): generate an object of class "ContIC". Rarely called directly.

show

signature(object = "ContIC")

Author(s)

Matthias Kohl [email protected]

References

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

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

See Also

IC-class, ContIC HampIC-class

Examples

IC1 <- new("ContIC")
plot(IC1)

Description

Generates an object of class "ContNeighborhood".

Usage

ContNeighborhood(radius = 0)

Arguments

Value

Object of class "ContNeighborhood"

Author(s)

Matthias Kohl [email protected]

References

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

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

See Also

ContNeighborhood-class

Examples

ContNeighborhood()

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

Description

Class of (unconditional) contamination neighborhoods.

Objects from the Class

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

Slots

type

Object of class "character": “(uncond.) convex contamination neighborhood”.

radius

Object of class "numeric": neighborhood radius.

Extends

Class "UncondNeighborhood", directly.
Class "Neighborhood", by class "UncondNeighborhood".

Methods

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

Author(s)

Matthias Kohl [email protected]

References

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

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

See Also

ContNeighborhood, UncondNeighborhood-class

Examples

new("ContNeighborhood")

Description

Generating function(s) for class cutoff.

Usage

cutoff(name = "empirical", body.fct0,
       cutoff.quantile  = 0.95,
       norm = NormType(), QF, nsim = 100000)
cutoff.sememp(cutoff.quantile = 0.95)
cutoff.chisq(cutoff.quantile = 0.95)
cutoff.quant(qfct)

Arguments

Details

cutoff generates a valid object of class "cutoff". As function slot fct may only have a formal argument data, the other arguments to determine the cutoff value, i.e. norm, QF, nsim, cutoff.quantile, nsim have to enter the scope of this function by lexical scoping; now cutoff.quantile, norm, QF are to be taken from the calling environment (not from the defining one), so we have delay evaluation of the function body, which is why we assume it to be given wrapped into substitute resp. quote. body.fct0 is by default (i.e. if argument body.fct0 is missing) set to
quote(quantile(slot(norm,"fct")(data), cutoff.quantile)), internally, i.e.; to an empirical quantile of the corresponding norms.

cutoff.sememp() is a helper function generating the theoretical (asymptotic) quantile of (the square root of) a corresponding quadratic form, assuming multivariate normality; to determine this quantile nsim simulations are used.

cutoff.chisq() is a helper function generating the theoretical (asymptotic) quantile of (the square root of) a (self-standardized) quadratic form, assuming multivariate normality; i.e.; a corresponding quantile of a Chi-Square distribution.

cutoff.quant() is a helper function generating the theoretical quantile corresponding to the quantile function qfct; if qfct is missing, it searches the caller environment for an object ..ICloc, and if this exists it uses the respective model quantile function; the fallback is qnorm. At any rate, if there is an object ..trf in the scope of the function it is used to transfer the quantile (after its evaluation).

Value

Object of class "cutoff".

Author(s)

Peter Ruckdeschel [email protected]

See Also

cutoff-class, ddPlot

Examples

cutoff()
cutoff.sememp()
cutoff.chisq()

Description

Class of methods to determine cutoff point for distance-distance plots; used to derive other cutoff methods later by method dispatch.

Objects from the Class

Objects could in principle be created by calls of the form new("cutoff", ...). More frequently they are created via the generating function cutoff, respectively via the helper functions cutoff.sememp and cutoff.chisq.

Slots

name:

object of class "character"; defaults to "empirical" in prototype;

fct:

an object of of class "function"; for this class layer, this function must only have one argument data (which may but need not be used to determine the cutoff point empirically); in derived classes this restriction could be dropped, if corresponding special methods for ddPlot are derived. Defaults to function(data) quantile(data).

cutoff.quantile:

Object of class "numeric": a probability (in [0,1]) to determine the respective quantile (empirical or theoretical) to plot the cutoff line; defaults to 0.95 in prototype;

Methods

cutoff.quantile

signature(object = "cutoff"): accessor function for slot cutoff.quantile.

cutoff.quantile<-

signature(object = "cutoff"): replacement function for slot cutoff.quantile.

fct

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

name

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

Author(s)

Peter Ruckdeschel [email protected]

See Also

ddPlot, outlyingPlotIC cutoff

Examples

cutoff()

Description

ddPlot-methods

Usage

ddPlot(data, dist.x, dist.y, cutoff.x, cutoff.y, ...)
## S4 method for signature 'matrix'
ddPlot(data, dist.x = NormType(), dist.y  = NormType(),
       cutoff.x, cutoff.y, ...,
       cutoff.quantile.x = 0.95, cutoff.quantile.y = cutoff.quantile.x,
       transform.x, transform.y = transform.x,
       id.n, cex.pts = 1,lab.pts, jitter.pts = 0, alpha.trsp = NA, adj =0, cex.idn,
       col.idn, lty.cutoff, lwd.cutoff, col.cutoff, text.abline = TRUE,
       text.abline.x = NULL, text.abline.y = NULL,
       cex.abline = par("cex"), col.abline = col.cutoff,
       font.abline = par("font"), adj.abline = c(0,0),
       text.abline.x.x = NULL, text.abline.x.y = NULL, 
       text.abline.y.x = NULL, text.abline.y.y = NULL,
       text.abline.x.fmt.cx = "%7.2f", text.abline.x.fmt.qx = "%4.2f%%",
       text.abline.y.fmt.cy = "%7.2f", text.abline.y.fmt.qy = "%4.2f%%", 
	     jitter.fac, jitter.tol = .Machine$double.eps,doplot = TRUE)
## S4 method for signature 'numeric'
ddPlot(data, dist.x = NormType(), dist.y  = NormType(),
       cutoff.x, cutoff.y, ...,
       cutoff.quantile.x = 0.95, cutoff.quantile.y = cutoff.quantile.x,
       transform.x, transform.y = transform.x,
       id.n, cex.pts = 1,lab.pts, jitter.pts = 0, alpha.trsp = NA, adj =0, cex.idn,
       col.idn, lty.cutoff, lwd.cutoff, col.cutoff, text.abline = TRUE,
       text.abline.x = NULL, text.abline.y = NULL,
       cex.abline = par("cex"), col.abline = col.cutoff,
       font.abline = par("font"), adj.abline = c(0,0),
       text.abline.x.x = NULL, text.abline.x.y = NULL, 
       text.abline.y.x = NULL, text.abline.y.y = NULL,
       text.abline.x.fmt.cx = "%7.2f", text.abline.x.fmt.qx = "%4.2f%%",
       text.abline.y.fmt.cy = "%7.2f", text.abline.y.fmt.qy = "%4.2f%%",
	   jitter.fac, jitter.tol=.Machine$double.eps, doplot = TRUE)
## S4 method for signature 'data.frame'
ddPlot(data, dist.x = NormType(), dist.y  = NormType(),
       cutoff.x, cutoff.y, ...,
       cutoff.quantile.x = 0.95, cutoff.quantile.y = cutoff.quantile.x,
       transform.x, transform.y = transform.x,
       id.n, cex.pts = 1,lab.pts, jitter.pts = 0, alpha.trsp = NA, adj =0, cex.idn,
       col.idn, lty.cutoff, lwd.cutoff, col.cutoff, text.abline = TRUE,
       text.abline.x = NULL, text.abline.y = NULL,
       cex.abline = par("cex"), col.abline = col.cutoff,
       font.abline = par("font"), adj.abline = c(0,0),
       text.abline.x.x = NULL, text.abline.x.y = NULL, 
       text.abline.y.x = NULL, text.abline.y.y = NULL,
       text.abline.x.fmt.cx = "%7.2f", text.abline.x.fmt.qx = "%4.2f%%",
       text.abline.y.fmt.cy = "%7.2f", text.abline.y.fmt.qy = "%4.2f%%",
	   jitter.fac, jitter.tol=.Machine$double.eps, doplot = TRUE)

Arguments

Details

The matrix-method calls .ddPlot.MatNtNtCoCo, the numeric- and data.frame-methods coerce argument data to matrix — the numeric-method by a call to matrix(data, nrow=1), in the data.frame-methods by a call to t(as.matrix(data)).

In arguments text.abline.x and text.abline.y the following patterns are substituted:

"%qx"

cutoff-quantile in x-direction

"%qy"

cutoff-quantile in y-direction

"%cx"

cutoff-value in x-direction

"%cy"

cutoff-value in y-direction

Value

If argument doplot is FALSE: A list (returned as invisible()) with items

If argument doplot is TRUE: 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. One item is retV which is the return value in case doplot is FALSE.

Author(s)

Peter Ruckdeschel [email protected]

Examples

MX <- matrix(rnorm(1500),nrow=6)
QM <- matrix(rnorm(36),nrow=6); QM <- QM %*% t(QM)
ddPlot(data=MX, dist.y=QFNorm(QuadF=PosSemDefSymmMatrix(QM)))

Description

Generic function for evaluating ICs.

Usage

evalIC(IC, x)

Arguments

Details

The list of random variables contained in the slot Curve is evaluated at x.

Value

In case x is numeric a vector and in case x is matrix a matrix is returned.

Author(s)

Matthias Kohl [email protected]

References

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

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

See Also

IC-class

Description

Generates an object of class "FixRobModel".

Usage

FixRobModel(center = ParamFamily(modifyParam = 
            function(theta) Norm(mean = theta)), neighbor = ContNeighborhood())

Arguments

Value

Object of class "FixRobModel"

Author(s)

Matthias Kohl [email protected]

References

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

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

See Also

FixRobModel-class

Examples

(M1 <- FixRobModel())

## The function is currently defined as
function(center = ParamFamily(), neighbor = ContNeighborhood()){
    new("FixRobModel", center = center, neighbor = neighbor)
}

Description

Class of robust models with fixed (unconditional) neighborhoods.

Objects from the Class

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

Slots

center

Object of class "ProbFamily".

neighbor

Object of class "UncondNeighborhood".

Extends

Class "RobModel", directly.

Methods

neighbor<-

signature(object = "FixRobModel"): replacement function for slot neighbor<-

show

signature(object = "FixRobModel")

Author(s)

Matthias Kohl [email protected]

References

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

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

See Also

ProbFamily-class, UncondNeighborhood-class, FixRobModel

Examples

new("FixRobModel")

Description

This function is rarely called directly. It is used by other functions to create objects of class "IC".

Usage

generateIC(neighbor, L2Fam, ...)

Arguments

Value

Object of class "IC"

Author(s)

Matthias Kohl [email protected]

References

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

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

See Also

IC-class, ContIC-class, TotalVarIC-class

Description

Generic function for providing centering and Fisher consistency of ICs.

Usage

generateIC.fct(neighbor, L2Fam, ...)

Arguments

Value

An IC at the model.

Methods

generateIC.fct

signature(IC = "UncondNeighborhood", L2Fam = "L2ParamFamily": ...

Author(s)

Peter Ruckdeschel [email protected]

References

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

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

See Also

L2ParamFamily-class, IC-class

Description

Generic function for the computation of the asymptotic bias for an IC.

Usage

getBiasIC(IC, neighbor, ...)

## S4 method for signature 'IC,UncondNeighborhood'
getBiasIC(IC, neighbor, L2Fam,
             biastype = symmetricBias(), normtype = NormType(),
             tol = .Machine$double.eps^0.25, numbeval = 1e5, withCheck = TRUE, ...)

Arguments

Value

The bias of the IC is computed.

Methods

IC = "IC", neighbor = "UncondNeighborhood"

determines the as. bias by random evaluation of the IC; this random evaluation is done by the internal S4-method .evalBiasIC; this latter dispatches according to the signature IC, neighbor, biastype.
For signature IC="IC", neighbor = "ContNeighborhood", biastype = "BiasType", also an argument normtype is used to be able to use self- or information standardizing norms; besides this the signatures IC="IC", neighbor = "TotalVarNeighborhood", biastype = "BiasType", IC="IC", neighbor = "ContNeighborhood", biastype = "onesidedBias", and IC="IC", neighbor = "ContNeighborhood", biastype = "asymmetricBias" are implemented.

Note

This generic function is still under construction.

Author(s)

Peter Ruckdeschel [email protected]

References

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

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

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

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

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

See Also

getRiskIC-methods, InfRobModel-class

Description

Generates a bounded influence curve.

Usage

getBoundedIC(L2Fam, D=trafo(L2Fam@param), ..., diagnostic = FALSE)

Arguments

Value

(a bounded) pIC (to matrix D) given as object of class "EuclRandVariable"

Author(s)

Peter Ruckdeschel [email protected]

References

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

Description

Generic function for the computation of finite-sample risks. This function is rarely called directly. It is used by other functions.

Usage

getFiRisk(risk, Distr, neighbor, ...)

## S4 method for signature 'fiUnOvShoot,Norm,ContNeighborhood'
getFiRisk(risk, Distr, 
          neighbor, clip, stand, sampleSize, Algo, cont)

## S4 method for signature 'fiUnOvShoot,Norm,TotalVarNeighborhood'
getFiRisk(risk, Distr, 
          neighbor, clip, stand, sampleSize, Algo, cont)

Arguments

Details

The computation of the finite-sample under-/overshoot risk is based on FFT. For more details we refer to Section 11.3 of Kohl (2005).

Value

The finite-sample risk is computed.

Methods

risk = "fiUnOvShoot", Distr = "Norm", neighbor = "ContNeighborhood"

computes finite-sample under-/overshoot risk in methods for function getFixRobIC.

risk = "fiUnOvShoot", Distr = "Norm", neighbor = "TotalVarNeighborhood"

computes finite-sample under-/overshoot risk in methods for function getFixRobIC.

Author(s)

Matthias Kohl [email protected]

References

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

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

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

See Also

fiRisk-class

Description

getRiskFctBV for a given object of S4 class asGRisk returns a function in bias and variance to compute the asymptotic risk.

Methods

getRiskFctBV

signature(risk = "asGRisk", biastype = "ANY"): returns an error that the respective method is not yet implemented.

getRiskFctBV

signature(risk = "asMSE", biastype = "ANY"): returns a function with arguments bias and variance to compute the asymptotic MSE for a given ALE at a situation where it has bias bias (including the radius!) and variance variance.

getRiskFctBV

signature(risk = "asSemivar", biastype = "onesidedBias"): returns a function with arguments bias and variance to compute the asymptotic semivariance error, i.e. $E[(S_n-\theta)_+^2]$ resp. $E[(S_n-\theta)_-^2]$, for a given ALE $S_n$ at a situation where it has one-sided bias bias (including the radius!) and variance variance.

getRiskFctBV

signature(risk = "asSemivar", biastype = "asymmetricBias"): returns a function with arguments bias and variance to compute the asymptotic semivariance error, i.e. $E[\nu_1 (S_n-\theta)_+^2+\nu_2(S_n-\theta)_-^2]$ for a given ALE $S_n$ at a situation where it has one-sided bias bias (including the radius!) and variance variance.

Examples

myrisk <- asMSE()
getRiskFctBV(myrisk)

Description

Generic function for the computation of a risk for an IC.

Usage

getRiskIC(IC, risk, neighbor, L2Fam, ...)

## S4 method for signature 'IC,asCov,missing,missing'
getRiskIC(IC, risk,
    tol = .Machine$double.eps^0.25, withCheck = TRUE, ...)

## S4 method for signature 'IC,asCov,missing,L2ParamFamily'
getRiskIC(IC, risk, L2Fam,
    tol = .Machine$double.eps^0.25, withCheck = TRUE, ..., diagnostic = FALSE)

## S4 method for signature 'IC,trAsCov,missing,missing'
getRiskIC(IC, risk,
    tol = .Machine$double.eps^0.25, withCheck = TRUE, ...)

## S4 method for signature 'IC,trAsCov,missing,L2ParamFamily'
getRiskIC(IC, risk, L2Fam,
    tol = .Machine$double.eps^0.25, withCheck = TRUE, ...)

## S4 method for signature 'IC,asBias,UncondNeighborhood,missing'
getRiskIC(IC, risk, neighbor,
    tol = .Machine$double.eps^0.25, withCheck = TRUE, ...)

## S4 method for signature 'IC,asBias,UncondNeighborhood,L2ParamFamily'
getRiskIC(IC, risk, neighbor, L2Fam,
    tol = .Machine$double.eps^0.25, withCheck = TRUE, ...)

## S4 method for signature 'IC,asMSE,UncondNeighborhood,missing'
getRiskIC(IC, risk, neighbor,
    tol = .Machine$double.eps^0.25, withCheck = TRUE, ...)

## S4 method for signature 'IC,asMSE,UncondNeighborhood,L2ParamFamily'
getRiskIC(IC, risk, neighbor, L2Fam,
    tol = .Machine$double.eps^0.25, withCheck = TRUE, ...)

## S4 method for signature 'TotalVarIC,asUnOvShoot,UncondNeighborhood,missing'
getRiskIC(IC, risk, neighbor)

## S4 method for signature 'IC,fiUnOvShoot,ContNeighborhood,missing'
getRiskIC(IC, risk, neighbor, sampleSize, Algo = "A", cont = "left")

## S4 method for signature 'IC,fiUnOvShoot,TotalVarNeighborhood,missing'
getRiskIC(IC, risk, neighbor, sampleSize, Algo = "A", cont = "left")

Arguments

Details

To make sure that the results are valid, it is recommended to include an additional check of the IC properties of IC using checkIC.

Value

The risk of an IC is computed.

Methods

IC = "IC", risk = "asCov", neighbor = "missing", L2Fam = "missing"

asymptotic covariance of IC.

IC = "IC", risk = "asCov", neighbor = "missing", L2Fam = "L2ParamFamily"

asymptotic covariance of IC under L2Fam.

IC = "IC", risk = "trAsCov", neighbor = "missing", L2Fam = "missing"

asymptotic covariance of IC.

IC = "IC", risk = "trAsCov", neighbor = "missing", L2Fam = "L2ParamFamily"

asymptotic covariance of IC under L2Fam.

IC = "IC", risk = "asBias", neighbor = "ContNeighborhood", L2Fam = "missing"

asymptotic bias of IC under convex contaminations; uses method getBiasIC.

IC = "IC", risk = "asBias", neighbor = "ContNeighborhood", L2Fam = "L2ParamFamily"

asymptotic bias of IC under convex contaminations and L2Fam; uses method getBiasIC.

IC = "IC", risk = "asBias", neighbor = "TotalVarNeighborhood", L2Fam = "missing"

asymptotic bias of IC in case of total variation neighborhoods; uses method getBiasIC.

IC = "IC", risk = "asBias", neighbor = "TotalVarNeighborhood", L2Fam = "L2ParamFamily"

asymptotic bias of IC under L2Fam in case of total variation neighborhoods; uses method getBiasIC.

IC = "IC", risk = "asMSE", neighbor = "UncondNeighborhood", L2Fam = "missing"

asymptotic mean square error of IC.

IC = "IC", risk = "asMSE", neighbor = "UncondNeighborhood", L2Fam = "L2ParamFamily"

asymptotic mean square error of IC under L2Fam.

IC = "TotalVarIC", risk = "asUnOvShoot", neighbor = "UncondNeighborhood", L2Fam = "missing"

asymptotic under-/overshoot risk of IC.

IC = "IC", risk = "fiUnOvShoot", neighbor = "ContNeighborhood", L2Fam = "missing"

finite-sample under-/overshoot risk of IC.

IC = "IC", risk = "fiUnOvShoot", neighbor = "TotalVarNeighborhood", L2Fam = "missing"

finite-sample under-/overshoot risk of IC.

Note

This generic function is still under construction.

Author(s)

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

References

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

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

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

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

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

See Also

getRiskIC, InfRobModel-class

Description

Generates weight functions of Hampel / BdSt type for different bias and norm types.

Usage

getweight(Weight, neighbor, biastype, ...)
minbiasweight(Weight, neighbor, biastype, ...)
## S4 method for signature 'HampelWeight,ContNeighborhood,BiasType'
getweight(Weight, neighbor, biastype, normW)
## S4 method for signature 'HampelWeight,ContNeighborhood,BiasType'
minbiasweight(Weight, neighbor, biastype, normW)
## S4 method for signature 'HampelWeight,ContNeighborhood,onesidedBias'
getweight(Weight, neighbor, biastype, ...)
## S4 method for signature 'HampelWeight,ContNeighborhood,onesidedBias'
minbiasweight(Weight, neighbor, biastype, ...)
## S4 method for signature 'HampelWeight,ContNeighborhood,asymmetricBias'
getweight(Weight, neighbor, biastype, ...)
## S4 method for signature 'HampelWeight,ContNeighborhood,asymmetricBias'
minbiasweight(Weight, neighbor, biastype, ...)
## S4 method for signature 'BdStWeight,TotalVarNeighborhood,BiasType'
getweight(Weight, neighbor, biastype, ...)
## S4 method for signature 'BdStWeight,TotalVarNeighborhood,BiasType'
minbiasweight(Weight, neighbor, biastype, ...)

Arguments

Details

These functions generate the weight function in slot weight in a corresp. object of class RobWeight and descendants.

Value

Object of class "HampelWeight" resp. "BdStWeight"

Methods

getweight

signature(Weight = "HampelWeight", neighbor = "ContNeighborhood", biastype = "BiasType") with additional argument biastype of class "BiasType": produces weight slot...

minbiasweight

signature(Weight = "HampelWeight", neighbor = "ContNeighborhood", biastype = "BiasType") with additional argument biastype of class "BiasType": produces weight slot...

getweight

signature(Weight = "HampelWeight", neighbor = "ContNeighborhood", biastype = "onesidedBias"): produces weight slot...

minbiasweight

signature(Weight = "HampelWeight", neighbor = "ContNeighborhood", biastype = "onesidedBias"): produces weight slot...

getweight

signature(Weight = "HampelWeight", neighbor = "ContNeighborhood", biastype = "asymmetricBias"): produces weight slot...

minbiasweight

signature(Weight = "HampelWeight", neighbor = "ContNeighborhood", biastype = "asymmetricBias"): produces weight slot...

getweight

signature(Weight = "BdStWeight", neighbor = "TotalVarNeighborhood", biastype = "BiasType"): produces weight slot...

minbiasweight

signature(Weight = "BdStWeight", neighbor = "TotalVarNeighborhood", biastype = "BiasType"): produces weight slot...

Author(s)

Peter Ruckdeschel [email protected]

References

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

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

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

See Also

BdStWeight-class, HampelWeight-class, IC-class

Description

Classes for weights of Hampel type.

Objects from the Class

Objects can be created by calls of the form new("HampelWeight", ...); to fill slot weight, you will use the generating functions getweight and minbiasweight.

Slots

name

Object of class "character"; inherited from class RobWeight.

weight

Object of class "function" — the weight function; inherited from class RobWeight.

clip

Object of class "numeric" — clipping bound(s); inherited from class BoundedWeight.

stand

Object of class "matrix" — standardization; inherited from class BdStWeight.

cent

Object of class "numeric" — centering.

Extends

Class "RobWeight", via class "BoundedWeight". Class "BoundedWeight", via class "BdStWeight". Class "BdStWeight", directly.

Methods

cent

signature(object = "HampelWeight"): accessor function for slot cent.

cent<-

signature(object = "HampelWeight", value = "matrix"): replacement function for slot cent. This replacement method should be used with great care, as the slot weight is not simultaneously updated and hence, this may lead to inconsistent objects.

Author(s)

Peter Ruckdeschel [email protected]

References

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

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

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

See Also

BdStWeight-class, BoundedWeight-class, RobWeight-class, IC, InfluenceCurve-class

Examples

## prototype
new("HampelWeight")

Description

Class of (partial) influence curves of Hampel (= total variation or contamination) type; used as common mother class for classes ContIC and TotalVarIC.

Objects from the Class

Objects can be created by calls of the form new("HampIC", ...).

Slots

CallL2Fam

object of class "call": creates an object of the underlying L2-differentiable parametric family.

name

object of class "character"

Curve

object of class "EuclRandVarList"

modifyIC

object of class "OptionalFunction": function of four arguments: (1) L2Fam an L2 parametric family (2) IC an optional influence curve, (3) withMakeIC a logical argument whether to enforce the IC side conditions by makeIC, and (4) ... for arguments to be passed to calls to E in makeIC. Returns an object of class "IC". This function is mainly used for internal computations!

Risks

object of class "list": list of risks; cf. RiskType-class.

Infos

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

stand

object of class "matrix": standardizing matrix.

weight

object of class "RobWeight": weight function

biastype

object of class "BiasType": bias type (symmetric/onsided/asymmetric)

normtype

object of class "NormType": norm type (Euclidean, information/self-standardized)

lowerCase

object of class "OptionalNumeric": optional constant for lower case solution.

neighborRadius

object of class "numeric": radius of the corresponding (unconditional) contamination neighborhood.

Extends

Class "IC", directly.
Class "InfluenceCurve", by class "IC".

Methods

stand

signature(object = "HampIC"): accessor function for slot stand.

weight

signature(object = "HampIC"): accessor function for slot weight.

biastype

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

normtype

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

lowerCase

signature(object = "HampIC"): accessor function for slot lowerCase.

neighborRadius

signature(object = "HampIC"): accessor function for slot neighborRadius.

neighborRadius<-

signature(object = "HampIC"): replacement function for slot neighborRadius.

neighborRadius

signature(object = "ANY"): returns NULL.

Author(s)

Peter Ruckdeschel [email protected]

References

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

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

See Also

IC-class

Examples

IC1 <- new("HampIC")
plot(IC1)

Description

Generates an object of class "IC".

Usage

IC(name, Curve = EuclRandVarList(RealRandVariable(Map = list(function(x){x}), 
                                        Domain = Reals())), 
   Risks, Infos, CallL2Fam = call("L2ParamFamily"), modifyIC = NULL)

Arguments

Value

Object of class "IC"

Author(s)

Matthias Kohl [email protected]

References

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

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

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

See Also

IC-class

Examples

IC1 <- IC()
plot(IC1)

Description

Class of (partial) influence curves.

Objects from the Class

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

Slots

CallL2Fam

Object of class "call": creates an object of the underlying L2-differentiable parametric family.

modifyIC

object of class "OptionalFunction": function of four arguments: (1) L2Fam an L2 parametric family (2) IC an optional influence curve, (3) withMakeIC a logical argument whether to enforce the IC side conditions by makeIC, and (4) ... for arguments to be passed to calls to E in makeIC. Returns an object of class "IC". This function is mainly used for internal computations!

name

Object of class "character".

Curve

Object of class "EuclRandVarList".

Risks

Object of class "list": list of risks; cf. RiskType-class.

Infos

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

Extends

Class "InfluenceCurve", directly.

Methods

CallL2Fam

signature(object = "IC"): accessor function for slot CallL2Fam.

CallL2Fam<-

signature(object = "IC"): replacement function for slot CallL2Fam.

modifyIC

signature(object = "IC"): accessor function for slot modifyIC.

checkIC

signature(IC = "IC", L2Fam = "missing"): check centering and Fisher consistency of IC assuming the L2-differentiable parametric family which can be generated via the slot CallL2Fam of IC.

checkIC

signature(IC = "IC", L2Fam = "L2ParamFamily"): check centering and Fisher consistency of IC assuming the L2-differentiable parametric family L2Fam.

evalIC

signature(IC = "IC", x = "numeric"): evaluate IC at x.

evalIC

signature(IC = "IC", x = "matrix"): evaluate IC at the rows of x.

infoPlot

signature(object = "IC"): Plot absolute and relative information of IC.

plot

signature(x = "IC", y = "missing")

show

signature(object = "IC")

Author(s)

Matthias Kohl [email protected]

References

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

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

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

See Also

InfluenceCurve-class, IC

Examples

IC1 <- new("IC")
plot(IC1)

Description

Generates an object of class "InfluenceCurve".

Usage

InfluenceCurve(name, Curve = EuclRandVarList(EuclRandVariable(Domain = Reals())), 
            Risks, Infos)

Arguments

Value

Object of class "InfluenceCurve"

Author(s)

Matthias Kohl [email protected]

References

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

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

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

See Also

InfluenceCurve-class

Examples

InfluenceCurve()

## The function is currently defined as
InfluenceCurve <- function(name, Curve = EuclRandVarList(EuclRandVariable(Domain = Reals())), 
                           Risks, Infos){
    if(missing(name))
        name <- "influence curve"
    if(missing(Risks))
        Risks <- list()
    if(missing(Infos))
        Infos <- matrix(c(character(0),character(0)), ncol=2,
                     dimnames=list(character(0), c("method", "message")))
    
    return(new("InfluenceCurve", name = name, Curve = Curve, 
               Risks = Risks, Infos = Infos))
}

Description

Class of influence curves (functions).

Objects from the Class

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

Slots

name

object of class "character"

Curve

object of class "EuclRandVarList"

Risks

object of class "list": list of risks; cf. RiskType-class.

Infos

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

Methods

name

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

name<-

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

Curve

signature(object = "InfluenceCurve"): accessor function for slot Curve.

Map

signature(object = "InfluenceCurve"): accessor function for slot Map of slot Curve.

Domain

signature(object = "InfluenceCurve"): accessor function for slot Domain of slot Curve.

Range

signature(object = "InfluenceCurve"): accessor function for slot Range of slot Curve.

Infos

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

Infos<-

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

addInfo<-

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

Risks

signature(object = "InfluenceCurve"): accessor function for slot Risks. By means of internal function .evalListRec recursively evaluates all non evaluated calls and writes back the evaluated calls to the calling envirionment.

Risks<-

signature(object = "InfluenceCurve"): replacement function for slot Risks.

addRisk<-

signature(object = "InfluenceCurve"): function to add a risk to slot Risks.

show

signature(object = "InfluenceCurve")

Author(s)

Matthias Kohl [email protected]

References

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

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

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

See Also

InfluenceCurve, RiskType-class

Examples

new("InfluenceCurve")

Description

Plot absolute and relative information of influence curves.

Usage

infoPlot(object,  ...)
## S4 method for signature 'IC'
infoPlot(object, data = NULL,
             ..., withSweave = getdistrOption("withSweave"),
             col = par("col"), lwd = par("lwd"), lty,
             colI = grey(0.5), lwdI = 0.7*par("lwd"), ltyI = "dotted",
             main = FALSE, inner = TRUE, sub = FALSE,
             col.inner = par("col.main"), cex.inner = 0.8,
             bmar = par("mar")[1], tmar = par("mar")[3],
             with.automatic.grid = TRUE,
             with.legend = TRUE, legend = NULL, legend.bg = "white",
             legend.location = "bottomright", legend.cex = 0.8,
             x.vec = NULL, scaleX = FALSE, scaleX.fct, scaleX.inv,
             scaleY = FALSE, scaleY.fct = pnorm, scaleY.inv=qnorm,
             scaleN = 9, x.ticks = NULL, y.ticks = NULL,
             mfColRow = TRUE, to.draw.arg = NULL,
             cex.pts = 1, cex.pts.fun = NULL, col.pts = par("col"),
             pch.pts = 19,
             cex.npts = 1, cex.npts.fun = NULL, col.npts = grey(.5),
             pch.npts = 20,
             jitter.fac = 1, with.lab = FALSE, cex.lbs = 1, adj.lbs = c(0, 0),
             col.lbs = col.pts, lab.pts = NULL, lab.font = NULL, alpha.trsp = NA,
             which.lbs = NULL, which.Order  = NULL, which.nonlbs = NULL,
             attr.pre = FALSE, return.Order = FALSE,
             ylab.abs = "absolute information",
             ylab.rel= "relative information",
             withSubst = TRUE)

Arguments

Details

Absolute information is defined as the square of the length of an IC. The relative information is defined as the absolute information of one component with respect to the absolute information of the whole IC; confer Section 8.1 of Kohl (2005).

Any parameters of plot.default may be passed on to this particular plot method.

For main-, inner, and subtitles given as arguments main, inner, and sub, top and bottom margins are enlarged to 5 resp. 6 by default but may also be specified by tmar / bmar arguments. If main / inner / sub are logical then if the respective argument is FALSE nothing is done/plotted, but if it is TRUE, we use a default main title taking up the calling arguments in case of main, default inner titles taking up the class and (named) parameter slots of arguments in case of inner, and a "generated on <data>"-tag in case of sub. Of course, if main / inner / sub are character, this is used for the title; in case of inner it is then checked whether it has correct length. If argument withSubst is TRUE, in all title and axis lable arguments, the following patterns are substituted:

"%C"

class of argument object

"%A"

deparsed argument object

"%D"

time/date-string when the plot was generated

If argument ... contains argument ylim, this may either be as in plot.default (i.e. a vector of length 2) or a vector of length 2*(number of plotted dimensions + e), where e is 1 or 0 depending on whether absolute information is plotted or not; in the case of longer length, if e is 1, the first two elements are the values for ylim in panel "Abs", while the last 2*(number of plotted dimensions) are the values for ylim for the plotted dimensions of the IC, one pair for each dimension.

Similarly, if argument ... contains arguments xaxt or yaxt, these may be vectorized, with one value for each of the panels to be plotted. This is useful for stacking panels over each other, using a common x-axis (see example below).

The ... argument may also contain an argument withbox which if TRUE warrants that even if xaxt and yaxt both are FALSE, a box is drawn around the respective panel.

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).

Value

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.

Author(s)

Matthias Kohl [email protected]

References

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

See Also

L2ParamFamily-class, IC-class

Examples

N <- NormLocationScaleFamily(mean=0, sd=1) 
IC1 <- optIC(model = N, risk = asCov())
infoPlot(IC1)

## don't run to reduce check time on CRAN

## selection of subpanels for plotting
par(mfrow=c(1,2))
infoPlot(IC1, mfColRow = FALSE, to.draw.arg=c("Abs","sd"))
infoPlot(IC1, mfColRow = FALSE, to.draw.arg=c("Abs","sd"), log="y")

infoPlot(IC1, mfColRow = FALSE, to.draw.arg=c("Abs","mean"), 
              panel.first= grid(), ylim = c(0,4), xlim = c(-6,6))
infoPlot(IC1, mfColRow = FALSE, to.draw.arg=c("Abs","mean"), 
              panel.first= grid(), ylim = c(0,4,-3,3), xlim = c(-6,6))

par(mfrow=c(1,3))
infoPlot(IC1, mfColRow = FALSE, panel.first= grid(),
         ylim = c(0,4,0,.3,0,.8), xlim=c(-6,6))
par(mfrow=c(1,1))

data <- r(N)(20)
par(mfrow=c(1,3))
infoPlot(IC1, data=data, mfColRow = FALSE, panel.first= grid(),
         with.lab = TRUE, cex.pts=2,
         which.lbs = c(1:4,15:20), which.Order = 1:6,
         return.Order = TRUE)
infoPlot(IC1, data=data[1:10], mfColRow = FALSE, panel.first= grid(),
         with.lab = TRUE, cex.pts=0.7)
par(mfrow=c(1,1))

ICr <- makeIC(list(function(x)sign(x),function(x)sign(abs(x)-qnorm(.75))),N)
data <- r(N)(600)
data.c <- c(data, 1000*data[1:30])
par(mfrow=c(3,1))
infoPlot(ICr, data=data.c, tmar=c(4.1,0,0), bmar=c(0,0,4.1),
         xaxt=c("n","n","s"), mfColRow = FALSE, panel.first= grid(),
         cex.pts=c(.9,.9), alpha.trsp=20, lwd=2, lwdI=1.5, col=3,
         col.pts=c(3,2), colI=2, pch.pts=c(20,20), inner=FALSE,
         scaleX = TRUE, scaleX.fct=pnorm, scaleX.inv=qnorm,
         scaleY=TRUE, scaleY.fct=function(x) pchisq(x,df=1),
         scaleY.inv=function(x)qchisq(x,df=1),legend.cex = 1.0)

Description

The wrapper InfoPlot (captial I!) takes most of arguments to the plot method infoPlot (lower case i!) by default and gives a user possibility to run the function with low number of arguments.

Usage

InfoPlot(IC, data, ..., alpha.trsp = 100,
    with.legend = TRUE, rescale = FALSE, withCall = TRUE)

Arguments

Value

invisible(retV) where retV is the return value of the respective call to the full-fledged function infoPlot with the additional item wrapcall with the call to the wrapper InfoPlot and wrappedcall the call to to the full-fledged function infoPlot.

Details

Calls infoPlot with suitably chosen defaults. If withCall == TRUE, the call to infoPlot, i.e., item wrappedcall of the (hidden) return value, is returned

Examples

# Gamma
fam  <-  GammaFamily()
IC <- optIC(model = fam, risk = asCov())
Y <- distribution(fam)
data  <-  r(Y)(500)
InfoPlot(IC, data, withCall = FALSE)

Description

Generates an object of class "InfRobModel".

Usage

InfRobModel(center = L2ParamFamily(), neighbor = ContNeighborhood())

Arguments

Value

Object of class "FixRobModel"

Author(s)

Matthias Kohl [email protected]

References

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

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

See Also

RobModel-class, FixRobModel-class

Examples

(M1 <- InfRobModel())

## The function is currently defined as
function(center = L2ParamFamily(), neighbor = ContNeighborhood()){
    new("InfRobModel", center = center, neighbor = neighbor)
}

Description

Class of robust models with infinitesimal (unconditional) neighborhoods; i.e., the neighborhood is shrinking at a rate of $\sqrt{n}$.

Objects from the Class

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

Slots

center

Object of class "ProbFamily".

neighbor

Object of class "UncondNeighborhood".

Extends

Class "RobModel", directly.

Methods

neighbor<-

signature(object = "InfRobModel"): replacement function for slot neighbor<-

show

signature(object = "InfRobModel")

Author(s)

Matthias Kohl [email protected]

References

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

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

See Also

ProbFamily-class, UncondNeighborhood-class, InfRobModel

Examples

new("InfRobModel")

Description

Class of risks for which algorithms dispatch to speed-up algorithms

Usage

MBRRisk(samplesize=100)
OMSRRisk(samplesize=100)
RMXRRisk(samplesize=100)

Arguments

Details

The main purpose of classes OMSRRisk, MBRRisk, and RMXRRisk is to help to dispatch into speed-up algorithms later in function roptest. In all these risks, we assume convex contamination neighborhoods. OMSRRisk stands for optimal MSE-robust estimation (where we assume a radius r of 0.5), RMXRRisk stands for optimal optimally RMX-robust estimation and MBRRisk stands for optimal Bias-robust estimation. All these risks have an additional slot samplesize, defaulting to 100, and for which there is a replacement and an accessor method.

Objects from the Class

interpolRisk is a virtual class: No objects may be created from it. the other classes are generated via generating functions.

Slots

type

Object of class "character": type of risk. (Inherited from RiskType).

Author(s)

Peter Ruckdeschel [email protected]

Examples

new("OMSRRisk")
OMSRRisk()
RMXRRisk()
MBRRisk()
myrisk <- MBRRisk(samplesize=100)
samplesize(myrisk)
samplesize(myrisk) <- 20

Description

Class of asymptotically linear estimates.

Objects from the Class

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

Slots

name

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

estimate

Object of class "ANY": estimate.

estimate.call

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

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.

asvar

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

asbias

Optional object of class "numeric": asymptotic bias.

pIC

Optional object of class InfluenceCurve: influence curve.

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.

steps

Object of class "integer": number of steps.

Infos

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

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.

pICList

Optional object of class "OptionalpICList": the list of (intermediate) (partial) influence curves used; only filled when called from kStepEstimator with argument withPICList==TRUE.

ICList

Optional object of class "OptionalpICList": the list of (intermediate) (total) influence curves used; only filled when called from kStepEstimator with argument withICList==TRUE.

start

The argument start — of class "StartClass" used in call to kStepEstimator.

startval

Object of class matrix: the starting value with which the k-step Estimator was initialized (in $p$-space / transformed).

ustartval

Object of class matrix: the starting value with which the k-step Estimator was initialized (in $k$-space / untransformed).

ksteps

Object of class "OptionalMatrix": the intermediate estimates (in $p$-space) for the parameter; only filled when called from kStepEstimator.

uksteps

Object of class "OptionalMatrix": the intermediate estimates (in $k$-space) for the parameter; only filled when called from kStepEstimator.

robestcall

Object of class "OptionalCall", i.e., a call or NULL: only filled when called from roptest in package ROptEst.

Extends

Class "ALEstimate", directly.
Class "Estimate", by class "ALEstimate"

Methods

steps

signature(object = "kStepEstimate"): accessor function for slot steps.

ksteps

signature(object = "kStepEstimate"): accessor function for slot ksteps; has additional argument diff, defaulting to FALSE; if the latter is TRUE, the starting value from slot startval is prepended as first column; otherwise we return the corresponding increments in each step.

uksteps

signature(object = "kStepEstimate"): accessor function for slot uksteps; has additional argument diff, defaulting to FALSE; if the latter is TRUE, the starting value from slot ustartval is prepended as first column; otherwise we return the corresponding increments in each step.

start

signature(object = "kStepEstimate"): accessor function for slot start.

startval

signature(object = "kStepEstimate"): accessor function for slot startval.

ustartval

signature(object = "kStepEstimate"): accessor function for slot startval.

ICList

signature(object = "kStepEstimate"): accessor function for slot ICList.

pICList

signature(object = "kStepEstimate"): accessor function for slot pICList.

robestCall

signature(object = "kStepEstimate"): accessor function for slot robestCall.

timings

signature(object = "kStepEstimate"): accessor function for attribute "timings".

show

signature(object = "kStepEstimate"): a show method;

Author(s)

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

See Also

ALEstimate-class

Description

Function for the computation of k-step estimates.

Usage

kStepEstimator(x, IC, start = NULL, steps = 1L,
      useLast = getRobAStBaseOption("kStepUseLast"),
      withUpdateInKer = getRobAStBaseOption("withUpdateInKer"),
      IC.UpdateInKer = getRobAStBaseOption("IC.UpdateInKer"),
      withICList = getRobAStBaseOption("withICList"),
      withPICList = getRobAStBaseOption("withPICList"),
      na.rm = TRUE, startArgList = NULL, ...,
      withLogScale = TRUE, withEvalAsVar = TRUE,
      withMakeIC = FALSE, E.argList = NULL, diagnostic = FALSE)

Arguments

Details

Given an initial estimation start, a sample x and an influence curve IC the corresponding k-step estimator is computed.

The default value of argument useLast is set by the global option kStepUseLast which by default is set to FALSE. In case of general models useLast remains unchanged during the computations. However, if slot CallL2Fam of IC generates an object of class "L2GroupParamFamily" the value of useLast is changed to TRUE. Explicitly setting useLast to TRUE should be done with care as in this situation the influence curve is re-computed using the value of the one-step estimate which may take quite a long time depending on the model.

If useLast is set to TRUE and slot modifyIC of IC is filled with some function (which can be used to re-compute the IC for a different parameter), the computation of asvar, asbias and IC is based on the k-step estimate.

Timings for the several substeps are available as attribute timings of the return value.

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.

Value