getInfStandRegTS: Generic Function for the Computation of the Standardizing Matrix

Description

Generic function for the computation of the standardizing matrix which takes care of the Fisher consistency of the corresponding IC. This function is rarely called directly. It is used to compute optimally robust ICs.

Usage

getInfStandRegTS(ErrorL2deriv, Regressor, neighbor, ...)
# S4 method for UnivariateDistribution,UnivariateDistribution,ContNeighborhood
getInfStandRegTS(
             ErrorL2deriv, Regressor, neighbor, z.comp, clip, cent, stand, trafo)
# S4 method for UnivariateDistribution,UnivariateDistribution,TotalVarNeighborhood
getInfStandRegTS(
             ErrorL2deriv, Regressor, neighbor, clip, cent)
# S4 method for UnivariateDistribution,UnivariateDistribution,CondTotalVarNeighborhood
getInfStandRegTS(
             ErrorL2deriv, Regressor, neighbor, clip, cent)
# S4 method for UnivariateDistribution,UnivariateDistribution,Av1CondContNeighborhood
getInfStandRegTS(
             ErrorL2deriv, Regressor, neighbor, z.comp, clip, cent, stand, trafo)
# S4 method for UnivariateDistribution,UnivariateDistribution,Av1CondTotalVarNeighborhood
getInfStandRegTS(
             ErrorL2deriv, Regressor, neighbor, z.comp, clip, cent, stand, trafo)
# S4 method for UnivariateDistribution,MultivariateDistribution,ContNeighborhood
getInfStandRegTS(
             ErrorL2deriv, Regressor, neighbor, z.comp, clip, cent, stand, trafo)
# S4 method for UnivariateDistribution,MultivariateDistribution,Av1CondContNeighborhood
getInfStandRegTS(
             ErrorL2deriv, Regressor, neighbor, z.comp, clip, cent, stand, trafo)
# S4 method for UnivariateDistribution,MultivariateDistribution,Av1CondTotalVarNeighborhood
getInfStandRegTS(
             ErrorL2deriv, Regressor, neighbor, z.comp, clip, cent, stand, trafo)
# S4 method for UnivariateDistribution,Distribution,Av2CondContNeighborhood
getInfStandRegTS(
             ErrorL2deriv, Regressor, neighbor, z.comp, clip, cent, stand, trafo)
# S4 method for RealRandVariable,Distribution,ContNeighborhood
getInfStandRegTS(
             ErrorL2deriv, Regressor, neighbor, ErrorDistr, A.comp, stand, clip,
             cent, trafo)
# S4 method for RealRandVariable,Distribution,Av1CondContNeighborhood
getInfStandRegTS(
             ErrorL2deriv, Regressor, neighbor, ErrorDistr, A.comp, stand, clip,
             cent, trafo)

Arguments

ErrorL2deriv

L2-derivative of ErrorDistr.

Regressor

regressor.

neighbor

object of class "Neighborhood".

…

additional parameters.

ErrorDistr

error distribution.

clip

optimal clipping bound/function.

cent

optimal centering constant/function.

stand

standardizing matrix.

z.comp

which components of the centering constant/function have to be computed.

A.comp

which components of the standardizing matrix have to be computed.

trafo

matrix: transformation of the parameter.

Value

The standardizing matrix is computed.

Methods

ErrorL2deriv = "UnivariateDistribution", Regressor = "UnivariateDistribution", neighbor = "ContNeighborhood": computes standardizing matrix.
ErrorL2deriv = "UnivariateDistribution", Regressor = "UnivariateDistribution", neighbor = "TotalVarNeighborhood": computes standardizing constant.
ErrorL2deriv = "UnivariateDistribution", Regressor = "UnivariateDistribution", neighbor = "CondTotalVarNeighborhood": computes standardizing constant.
ErrorL2deriv = "UnivariateDistribution", Regressor = "UnivariateDistribution", neighbor = "Av1CondContNeighborhood": computes standardizing matrix.
ErrorL2deriv = "UnivariateDistribution", Regressor = "UnivariateDistribution", neighbor = "Av1CondTotalVarNeighborhood": computes standardizing matrix.
ErrorL2deriv = "UnivariateDistribution", Regressor = "MultivariateDistribution", neighbor = "ContNeighborhood": computes standardizing matrix.
ErrorL2deriv = "UnivariateDistribution", Regressor = "MultivariateDistribution", neighbor = "Av1CondContNeighborhood": computes standardizing matrix.
ErrorL2deriv = "UnivariateDistribution", Regressor = "MultivariateDistribution", neighbor = "Av1CondTotalVarNeighborhood": computes standardizing matrix.
ErrorL2deriv = "UnivariateDistribution", Regressor = "Distribution", neighbor = "Av2CondContNeighborhood": computes standardizing matrix.
ErrorL2deriv = "RealRandVariable", Regressor = "Distribution", neighbor = "ContNeighborhood": computes standardizing matrix.
ErrorL2deriv = "RealRandVariable", Regressor = "Distribution", neighbor = "Av1CondContNeighborhood": computes standardizing matrix.

References

Rieder, H. (1980) Estimates derived from robust tests. Ann. Stats. 8: 106--115.

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

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