L2ParamFamily: 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)

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, star

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 par

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 m

L2derivSymm

object of class "FunSymmList": symmetry of the maps contained in L2deriv

L2derivDistr

object of class "UnivarDistrList": distribution of L2deriv

L2derivDistrSymm

object of class "DistrSymmList": symmetry of the distributions contained in L2derivDistr

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 Fi

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 produce objects of class Binomia

Value

Object of class "L2ParamFamily"

concept

parametric family

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.

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer. Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

Examples

Run this code

F1 <- L2ParamFamily()
plot(F1)

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