ALEstimate-class.
Class of asymptotically linear estimates.
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 can be created by calls of the form new("ALEstimate", ...).
nameObject of class "character":
name of the estimator.
estimateObject of class "ANY":
estimate.
estimate.callObject 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.
asvarobject of class "OptionalNumericOrMatrix"
which may contain the asymptotic (co)variance of the estimator.
asbiasOptional object of class "numeric":
asymptotic bias.
pICOptional 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.estimateObject of class "ANY":
untransformed estimate.
untransformed.asvar object of class "OptionalNumericOrMatrix"
which may contain the asymptotic (co)variance of the untransformed
estimator.
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.
signature(object = "ALEstimate"):
accessor function for slot pIC.
signature(object = "ALEstimate")
signature(object = "ALEstimate", method = "missing"):
compute asymptotic (LAN-based) confidence interval neglecting any bias.
signature(object = "ALEstimate", method = "symmetricBias"):
compute asymptotic (LAN-based) confidence interval incorporating bias
symmetrically.
signature(object = "ALEstimate", method = "onesidedBias"):
compute asymptotic (LAN-based) confidence interval incorporating bias
one-sided; i.e., positive or negative, respectively.
signature(object = "ALEstimate", method = "asymmetricBias"):
compute asymptotic (LAN-based) confidence interval incorporating bias
asymmetrically.
Matthias Kohl Matthias.Kohl@stamats.de and Peter Ruckdeschel Peter.Ruckdeschel@uni-oldenburg.de
## 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 filledPlease choose more modern alternatives, such as Google Chrome or Mozilla Firefox.