distrMod (version 2.9.4)

MCEstimator: 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)

Value

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

"Estimate".

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.

Author

Matthias Kohl ,
Peter Ruckdeschel

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.

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")