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

Description

Generic function for the computation of the optimal clipping bound in case of infinitesimal robust models. This function is rarely called directly. It is used to compute optimally robust ICs.

Usage

getInfClip(clip, L2deriv, risk, neighbor, ...)
# S4 method for numeric,UnivariateDistribution,asMSE,ContNeighborhood
getInfClip(
     clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo)
# S4 method for numeric,UnivariateDistribution,asMSE,TotalVarNeighborhood
getInfClip(
     clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo)
# S4 method for numeric,UnivariateDistribution,asL1,ContNeighborhood
getInfClip(
     clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo)
# S4 method for numeric,UnivariateDistribution,asL1,TotalVarNeighborhood
getInfClip(
     clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo)
# S4 method for numeric,UnivariateDistribution,asL4,ContNeighborhood
getInfClip(
     clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo)
# S4 method for numeric,UnivariateDistribution,asL4,TotalVarNeighborhood
getInfClip(
     clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo)
# S4 method for numeric,EuclRandVariable,asMSE,UncondNeighborhood
getInfClip(
     clip, L2deriv, risk, neighbor, biastype, Distr, stand, cent, trafo, ...)
# S4 method for numeric,UnivariateDistribution,asUnOvShoot,UncondNeighborhood
getInfClip(
     clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo)
# S4 method for numeric,UnivariateDistribution,asSemivar,ContNeighborhood
getInfClip(
     clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo,...)

Value

The optimal clipping bound is computed.

Arguments

clip: positive real: clipping bound
L2deriv: L2-derivative of some L2-differentiable family of probability measures.
risk: object of class "RiskType".
neighbor: object of class "Neighborhood".
...: additional parameters, in particular for expectation E
biastype: object of class "BiasType"
cent: optimal centering constant.
stand: standardizing matrix.
Distr: object of class "Distribution".
symm: logical: indicating symmetry of L2deriv.
trafo: matrix: transformation of the parameter.

Methods

clip = "numeric", L2deriv = "UnivariateDistribution", risk = "asMSE", neighbor = "ContNeighborhood": optimal clipping bound for asymtotic mean square error.
clip = "numeric", L2deriv = "UnivariateDistribution", risk = "asMSE", neighbor = "TotalVarNeighborhood": optimal clipping bound for asymtotic mean square error.
clip = "numeric", L2deriv = "EuclRandVariable", risk = "asMSE", neighbor = "UncondNeighborhood": optimal clipping bound for asymtotic mean square error.
clip = "numeric", L2deriv = "UnivariateDistribution", risk = "asL1", neighbor = "ContNeighborhood": optimal clipping bound for asymtotic mean absolute error.
clip = "numeric", L2deriv = "UnivariateDistribution", risk = "asL1", neighbor = "TotalVarNeighborhood": optimal clipping bound for asymtotic mean absolute error.
clip = "numeric", L2deriv = "UnivariateDistribution", risk = "asL4", neighbor = "ContNeighborhood": optimal clipping bound for asymtotic mean power 4 error.
clip = "numeric", L2deriv = "UnivariateDistribution", risk = "asL4", neighbor = "TotalVarNeighborhood": optimal clipping bound for asymtotic mean power 4 error.
clip = "numeric", L2deriv = "UnivariateDistribution", risk = "asUnOvShoot", neighbor = "UncondNeighborhood": optimal clipping bound for asymtotic under-/overshoot risk.
clip = "numeric", L2deriv = "UnivariateDistribution", risk = "asSemivar", neighbor = "ContNeighborhood": optimal clipping bound for asymtotic semivariance.

Author

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

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 22, 201-223.

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.