L2ParamFamily {distrMod}

Generating function for L2ParamFamily-class

Description

Generates an object of class "L2ParamFamily".

Usage

L2ParamFamily(name, distribution = Norm(), distrSymm, 
              main = main(param), nuisance = nuisance(param),
              fixed = fixed(param), trafo = trafo(param),
              param = ParamFamParameter(name = paste("Parameter of", name),  
                          main = main, nuisance = nuisance, 
                          fixed = fixed, trafo = trafo),
              props = character(0),
              startPar = NULL, makeOKPar = NULL,
              modifyParam = function(theta){ Norm(mean=theta) },
              L2deriv.fct = function(param) {force(theta <- param@main)
                           return(function(x) {x-theta})},
              L2derivSymm, L2derivDistr, L2derivDistrSymm, 
              FisherInfo.fct, FisherInfo = FisherInfo.fct(param),
              .returnClsName = NULL, .withMDE = TRUE)

Arguments

name

character string: name of the family

distribution

object of class "Distribution": member of the family

distrSymm

object of class "DistributionSymmetry": symmetry of distribution.

main

numeric vector: main parameter

nuisance

numeric vector: nuisance parameter

fixed

numeric vector: fixed part of the parameter

trafo

function in param or matrix: transformation of the parameter

param

object of class "ParamFamParameter": parameter of the family

startPar

startPar is a function in the observations x returning initial information for MCEstimator used by optimize resp. optim; i.e; if (total) parameter is of length 1, startPar returns a search interval, else it returns an initial parameter value.

makeOKPar

makeOKPar is a function in the (total) parameter param; used if optim resp. optimize— try to use “illegal” parameter values; then makeOKPar makes a valid parameter value out of the illegal one; if NULL slot makeOKPar of ParamFamily is used to produce it.

modifyParam

function: mapping from the parameter space (represented by "param") to the distribution space (represented by "distribution").

props

character vector: properties of the family

L2deriv.fct

function: mapping from the parameter space (argument param of class "ParamFamParameter") to a mapping from observation x to the value of the L2derivative; L2deriv.fct is used by modifyModel to move the L2deriv according to a change in the parameter, and to fill slot L2deriv. More specifically, let us call the parts main and nuisance of the parameter the unknown parameter. If this unknown parameter is one-dimensional, the return value of L2deriv.fct must be a function in argument x, which is vectorized, (i.e., callable for a vector-valued x), and has a one-dimensional, numeric return value. In case the dimension of the unknown parameter is larger than one, the return value must be a list of functions, each of which satisfies the conditions formulated for the case of a one-dimensional parameter of interest. The order of the components of this list is the same as the order of the parameter coordinates in main, followed by the ones in nuisance.

L2derivSymm

object of class "FunSymmList": symmetry of the maps contained in L2deriv; a list of symmetry properties of the same length as the return value of L2deriv.fct .

L2derivDistr

object of class "UnivarDistrList": distribution of L2deriv; the length of this list of univariate distributions must be of the same length as the return value of L2deriv.fct .

L2derivDistrSymm

object of class "DistrSymmList": symmetry of the distributions contained in L2derivDistr; the length of this list of symmetry properties must be of the same length as the return value of L2deriv.fct .

FisherInfo.fct

function: mapping from the parameter space (argument param of class "ParamFamParameter") to the set of positive semidefinite matrices; FisherInfo.fct is used by modifyModel to move the Fisher information according to a change in the parameter

FisherInfo

object of class "PosSemDefSymmMatrix": Fisher information of the family

.returnClsName

the class name of the return value; by default this argument is NULL whereupon the return class will be L2ParamFamily; but, internally, this generating function is also used to e.g. produce objects of class BinomialFamily, PoisFamily GammaFamily, BetaFamily.

.withMDE

logical of length 1: Tells R how to use the function from slot startPar in case of a kStepEstimator—use it as is or to compute the starting point for a minimum distance estimator which in turn then serves as starting point for roptest / robest (from package ROptEst). If TRUE (default) the latter alternative is used. Ignored if ROptEst is not used.

Details

If name is missing, the default “L2 differentiable parametric family of probability measures” is used. In case distrSymm is missing it is set to NoSymmetry(). If param is missing, the parameter is created via main, nuisance and trafo as described in ParamFamParameter. In case L2derivSymm is missing, it is filled with an object of class FunSymmList with entries NonSymmetric(). In case L2derivDistr is missing, it is computed via imageDistr. If L2derivDistrSymm is missing, it is set to an object of class DistrSymmList with entries NoSymmetry(). In case FisherInfo is missing, it is computed from L2deriv using E.

Value

Object of class "L2ParamFamily"

Author(s)

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

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

L2ParamFamily-class

Examples

F1 <- L2ParamFamily()
plot(F1)