distrMod (version 2.0.1)

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.

See Also

L2ParamFamily-class

Examples

Run this code
F1 <- L2ParamFamily()
plot(F1)

Run the code above in your browser using DataCamp Workspace