ALEstimate-class {RobAStBase}

ALEstimate-class.

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 [e-mail] and Peter Ruckdeschel [e-mail]

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