distrMod (version 2.1.1)

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 = 0, validity.check = TRUE, asvar.fct, ...)

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 startP

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 (th

...

further arguments to criterion or optimize or optim, respectively.

Value

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

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

## 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")