getInfGammaRegTS: 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 getInfClipRegTS to compute optimally robust ICs.

Usage

getInfGammaRegTS(ErrorL2deriv, Regressor, risk, neighbor, ...)
# S4 method for UnivariateDistribution,UnivariateDistribution,asMSE,ContNeighborhood
getInfGammaRegTS(
             ErrorL2deriv, Regressor, risk, neighbor, z.comp, stand, cent, clip)
# S4 method for UnivariateDistribution,UnivariateDistribution,asMSE,Av1CondContNeighborhood
getInfGammaRegTS(
             ErrorL2deriv, Regressor, risk, neighbor, z.comp, stand, cent, clip)
# S4 method for UnivariateDistribution,UnivariateDistribution,asMSE,Av1CondTotalVarNeighborhood
getInfGammaRegTS(
             ErrorL2deriv, Regressor, risk, neighbor, z.comp, stand, cent, clip)
# S4 method for UnivariateDistribution,MultivariateDistribution,asMSE,ContNeighborhood
getInfGammaRegTS(
             ErrorL2deriv, Regressor, risk, neighbor, z.comp, stand, cent, clip)
# S4 method for UnivariateDistribution,MultivariateDistribution,asMSE,Av1CondContNeighborhood
getInfGammaRegTS(
             ErrorL2deriv, Regressor, risk, neighbor, z.comp, stand, cent, clip)
# S4 method for UnivariateDistribution,MultivariateDistribution,asMSE,Av1CondTotalVarNeighborhood
getInfGammaRegTS(
             ErrorL2deriv, Regressor, risk, neighbor, z.comp, stand, cent, clip)
# S4 method for UnivariateDistribution,Distribution,asMSE,Av2CondContNeighborhood
getInfGammaRegTS(
             ErrorL2deriv, Regressor, risk, neighbor, z.comp, stand, cent, clip)
# S4 method for RealRandVariable,Distribution,asMSE,ContNeighborhood
getInfGammaRegTS(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorDistr, stand, cent,
             clip)
# S4 method for RealRandVariable,Distribution,asMSE,Av1CondContNeighborhood
getInfGammaRegTS(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorDistr, stand, cent,
             clip)
# S4 method for UnivariateDistribution,UnivariateDistribution,asUnOvShoot,ContNeighborhood
getInfGammaRegTS(
             ErrorL2deriv, Regressor, risk, neighbor, cent, clip)
# S4 method for UnivariateDistribution,UnivariateDistribution,asUnOvShoot,TotalVarNeighborhood
getInfGammaRegTS(
             ErrorL2deriv, Regressor, risk, neighbor, cent, clip)
# S4 method for UnivariateDistribution,numeric,asUnOvShoot,CondContNeighborhood
getInfGammaRegTS(
             ErrorL2deriv, Regressor, risk, neighbor, clip)
# S4 method for UnivariateDistribution,numeric,asUnOvShoot,CondTotalVarNeighborhood
getInfGammaRegTS(
             ErrorL2deriv, Regressor, risk, neighbor, clip)

Arguments

ErrorL2deriv

L2-derivative of ErrorDistr.

Regressor

regressor.

risk

object of class "RiskType".

neighbor

object of class "Neighborhood".

…

additional parameters.

clip

optimal clipping bound.

cent

optimal centering constant/function.

stand

standardizing matrix.

z.comp

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

ErrorDistr

error distribution.

Methods

ErrorL2deriv = "UnivariateDistribution", Regressor = "UnivariateDistribution", risk = "asMSE", neighbor = "ContNeighborhood": used by getInfClipRegTS.
ErrorL2deriv = "UnivariateDistribution", Regressor = "UnivariateDistribution", risk = "asMSE", neighbor = "Av1CondContNeighborhood": used by getInfClipRegTS.
ErrorL2deriv = "UnivariateDistribution", Regressor = "UnivariateDistribution", risk = "asMSE", neighbor = "Av1CondTotalVarNeighborhood": used by getInfClipRegTS.
ErrorL2deriv = "UnivariateDistribution", Regressor = "MultivariateDistribution", risk = "asMSE", neighbor = "ContNeighborhood": used by getInfClipRegTS.
ErrorL2deriv = "UnivariateDistribution", Regressor = "MultivariateDistribution", risk = "asMSE", neighbor = "Av1CondContNeighborhood": used by getInfClipRegTS.
ErrorL2deriv = "UnivariateDistribution", Regressor = "MultivariateDistribution", risk = "asMSE", neighbor = "Av1CondTotalVarNeighborhood": used by getInfClipRegTS.
ErrorL2deriv = "UnivariateDistribution", Regressor = "Distribution", risk = "asMSE", neighbor = "Av2CondContNeighborhood": used by getInfClipRegTS.
ErrorL2deriv = "RealRandVariable", Regressor = "Distribution", risk = "asMSE", neighbor = "ContNeighborhood": used by getInfClipRegTS.
ErrorL2deriv = "RealRandVariable", Regressor = "Distribution", risk = "asMSE", neighbor = "Av1CondContNeighborhood": used by getInfClipRegTS.
ErrorL2deriv = "UnivariateDistribution", Regressor = "UnivariateDistribution", risk = "asUnOvShoot", neighbor = "ContNeighborhood": used by getInfClipRegTS.
ErrorL2deriv = "UnivariateDistribution", Regressor = "UnivariateDistribution", risk = "asUnOvShoot", neighbor = "TotalVarNeighborhood": used by getInfClipRegTS.
ErrorL2deriv = "UnivariateDistribution", Regressor = "numeric", risk = "asUnOvShoot", neighbor = "CondContNeighborhood": used by getInfClipRegTS.
ErrorL2deriv = "UnivariateDistribution", Regressor = "numeric", risk = "asUnOvShoot", neighbor = "CondTotalVarNeighborhood": used by getInfClipRegTS.

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.