getInfGamma: Generic Function for the Computation of the Optimal Clipping Bound

Description

Generic function for the computation of the optimal clipping bound. This function is rarely called directly. It is called by getInfClip to compute optimally robust ICs.

Usage

getInfGamma(L2deriv, risk, neighbor, ...)
# S4 method for UnivariateDistribution,asMSE,ContNeighborhood
getInfGamma(L2deriv, risk, neighbor, cent, clip)
# S4 method for UnivariateDistribution,asGRisk,TotalVarNeighborhood
getInfGamma(L2deriv, risk, neighbor, cent, clip)
# S4 method for RealRandVariable,asMSE,ContNeighborhood
getInfGamma(L2deriv, risk, neighbor, Distr, stand, cent, clip)
# S4 method for UnivariateDistribution,asUnOvShoot,ContNeighborhood
getInfGamma(L2deriv, risk, neighbor, cent, clip)

Arguments

L2deriv

L2-derivative of some L2-differentiable family of probability measures.

risk

object of class "RiskType".

neighbor

object of class "Neighborhood".

…

additional parameters

cent

optimal centering constant.

clip

optimal clipping bound.

stand

standardizing matrix.

Distr

object of class "Distribution".

Methods

L2deriv = "UnivariateDistribution", risk = "asMSE", neighbor = "ContNeighborhood": used by getInfClip.
L2deriv = "UnivariateDistribution", risk = "asGRisk", neighbor = "TotalVarNeighborhood": used by getInfClip.
L2deriv = "RealRandVariable", risk = "asMSE", neighbor = "ContNeighborhood": used by getInfClip.
L2deriv = "UnivariateDistribution", risk = "asUnOvShoot", neighbor = "ContNeighborhood": used by getInfClip.

Details

The function is used in case of asymptotic G-risks; confer Ruckdeschel and Rieder (2004).

References

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

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

Ruckdeschel, P. and Rieder, H. (2004) Optimal Influence Curves for General Loss Functions. Statistics & Decisions (submitted).

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