L2ParamFamily: Generating function for L2ParamFamily-class

In ROptEstOld: Optimally Robust Estimation - Old Version

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)

Matthias Kohl [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)

ROptEstOld documentation built on Feb. 4, 2024, 3 p.m.