getInfStand {ROptEst}

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 signature 'UnivariateDistribution,ContNeighborhood,BiasType'
getInfStand(L2deriv, 
     neighbor, biastype, clip, cent, trafo)

## S4 method for signature 
## 'UnivariateDistribution,TotalVarNeighborhood,BiasType'
getInfStand(L2deriv, 
     neighbor, biastype, clip, cent, trafo)

## S4 method for signature 'RealRandVariable,UncondNeighborhood,BiasType'
getInfStand(L2deriv,
     neighbor, biastype, Distr, A.comp, cent, trafo, w, ...)

## S4 method for signature 
## 'UnivariateDistribution,ContNeighborhood,onesidedBias'
getInfStand(L2deriv,
     neighbor, biastype, clip, cent, trafo, ...)

## S4 method for signature 
## 'UnivariateDistribution,ContNeighborhood,asymmetricBias'
getInfStand(L2deriv,
     neighbor, biastype, clip, cent, trafo)

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.

Value

The standardizing matrix is computed.

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(s)

Matthias Kohl [e-mail], Peter Ruckdeschel [e-mail]

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.

See Also

ContIC-class, TotalVarIC-class