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L2ParamFamily

Generating function for L2ParamFamily-class

Description

Generates an object of class "L2ParamFamily".

Usage

L2ParamFamily(name, distribution = Norm(), distrSymm,
        main = 0, nuisance, trafo, param, props = character(0), 
        L2deriv = EuclRandVarList(RealRandVariable(list(function(x) {x}), 
                                                   Domain = Reals())), 
        L2derivSymm, L2derivDistr, L2derivDistrSymm, FisherInfo)

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

trafo

matrix: transformation of the parameter

param

object of class "ParamFamParameter": parameter of the family

props

character vector: properties of the family

L2deriv

object of class "EuclRandVariable": L2 derivative of the family

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

object of class "PosDefSymmMatrix": Fisher information of the 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.

Value

Object of class "L2ParamFamily"

Author(s)

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

Examples

F1 <- L2ParamFamily()
plot(F1)
ROptEstOld

Optimally Robust Estimation - Old Version

v1.2.0
LGPL-3
Authors
Matthias Kohl [aut, cre, cph]
Initial release
2019-04-02

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