MCEstimator {distrMod}

Function to compute minimum criterion estimates

Description

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

Usage

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

Arguments

x

(empirical) data

ParamFamily

object of class "ParamFamily"

criterion

function: criterion to minimize; see Details section.

crit.name

optional name for criterion.

startPar

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

Infos

character: optional informations about estimator

trafo

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

penalty

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

validity.check

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

asvar.fct

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

na.rm

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

...

further arguments to criterion or optimize or optim, respectively.

.withEvalAsVar

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

nmsffx

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

.with.checkEstClassForParamFamily

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

Details

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

Value

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

Note

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

Author(s)

Matthias Kohl [e-mail],
Peter Ruckdeschel [e-mail]

See Also

ParamFamily-class, ParamFamily, MCEstimate-class

Examples

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

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

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

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

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

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

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

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

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