getInfStand: 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

getInfStand(L2deriv, neighbor, biastype, ...)
# S4 method for UnivariateDistribution,ContNeighborhood,BiasType
getInfStand(L2deriv, 
     neighbor, biastype, clip, cent, trafo)
# S4 method for UnivariateDistribution,TotalVarNeighborhood,BiasType
getInfStand(L2deriv, 
     neighbor, biastype, clip, cent, trafo)
# S4 method for RealRandVariable,UncondNeighborhood,BiasType
getInfStand(L2deriv,
     neighbor, biastype, Distr, A.comp, cent, trafo, w, ...)
# S4 method for UnivariateDistribution,ContNeighborhood,onesidedBias
getInfStand(L2deriv,
     neighbor, biastype, clip, cent, trafo, ...)
# S4 method for UnivariateDistribution,ContNeighborhood,asymmetricBias
getInfStand(L2deriv,
     neighbor, biastype, clip, cent, trafo)

Value

The standardizing matrix is computed.

Arguments

L2deriv: L2-derivative of some L2-differentiable family of probability measures.
neighbor: object of class "Neighborhood".
biastype: object of class "BiasType".
...: additional parameters, in particular for expectation E.
clip: optimal clipping bound.
cent: optimal centering constant.
Distr: object of class "Distribution".
trafo: matrix: transformation of the parameter.
A.comp: matrix: indication which components of the standardizing matrix have to be computed.
w: object of class RobWeight; current weight.

Methods

L2deriv = "UnivariateDistribution", neighbor = "ContNeighborhood", biastype = "BiasType": computes standardizing matrix for symmetric bias.
L2deriv = "UnivariateDistribution", neighbor = "TotalVarNeighborhood", biastype = "BiasType": computes standardizing matrix for symmetric bias.
L2deriv = "RealRandVariable", neighbor = "UncondNeighborhood", biastype = "BiasType": computes standardizing matrix for symmetric bias.
L2deriv = "UnivariateDistribution", neighbor = "ContNeighborhood", biastype = "onesidedBias": computes standardizing matrix for onesided bias.
L2deriv = "UnivariateDistribution", neighbor = "ContNeighborhood", biastype = "asymmetricBias": computes standardizing matrix for asymmetric bias.

Author

Matthias Kohl Matthias.Kohl@stamats.de, Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

References

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

Ruckdeschel, P. (2005) Optimally One-Sided Bounded Influence Curves. Mathematical Methods in Statistics 14(1), 105-131.

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