distrMod (version 2.0.7)

MDEstimator: Function to compute minimum distance estimates

Description

The function MDEstimator provides a general way to compute minimum distance estimates.

Usage

MDEstimator(x, ParamFamily, distance = KolmogorovDist, dist.name, 
            startPar = NULL,  Infos, trafo = NULL, 
            penalty = 0, asvar.fct, ...)

Arguments

x

(empirical) data

ParamFamily

object of class "ParamFamily"

distance

(generic) function: to compute distance beetween (emprical) data and objects of class "Distribution".

dist.name

optional name of distance

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

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 distance has to be a (generic) function with arguments the empirical data as well as an object of class "Distribution" and possibly ...; e.g. KolmogorovDist (default), TotalVarDist or HellingerDist. Uses mceCalc for method dispatch.

References

Huber, P.J. (1981) Robust Statistics. New York: Wiley. Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

See Also

ParamFamily-class, ParamFamily, MCEstimator, MCEstimate-class, fitdistr

Examples

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

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

## Kolmogorov(-Smirnov) minimum distance estimator
MDEstimator(x = x, ParamFamily = G, distance = KolmogorovDist)

## von Mises minimum distance estimator with default mu
MDEstimator(x = x, ParamFamily = G, distance = CvMDist)

## von Mises minimum distance estimator with default mu
MDEstimator(x = x, ParamFamily = G, distance = CvMDist,
            asvar.fct = distrMod:::.CvMMDCovariance)
#*** variance routine is still in testing phase so not yet
#*** exported to namespace
## von Mises minimum distance estimator with mu = N(0,1)
MDEstimator(x = x, ParamFamily = G, distance = CvMDist, mu = Norm())

## Total variation minimum distance estimator
## gamma distributions are discretized
MDEstimator(x = x, ParamFamily = G, distance = TotalVarDist)
## or smoothing of emprical distribution (takes some time!)
#MDEstimator(x = x, ParamFamily = G, distance = TotalVarDist, asis.smooth.discretize = "smooth")

## Hellinger minimum distance estimator
## gamma distributions are discretized
distroptions(DistrResolution = 1e-10)
MDEstimator(x = x, ParamFamily = G, distance = HellingerDist, startPar = c(1,2))
distroptions(DistrResolution = 1e-6) # default
## or smoothing of emprical distribution (takes some time!)
#MDEstimator(x = x, ParamFamily = G, distance = HellingerDist, asis.smooth.discretize = "smooth")