getInfCentRegTS: Generic Function for the Computation of the Optimal Centering Constant/Function resp. Lower Clipping Bound/Function

Description

Generic function for the computation of the optimal centering constant/function (contamination neighborhoods) respectively, of the optimal lower clipping bound/function (total variation neighborhoods). This function is rarely called directly. It is used to compute optimally robust ICs.

Usage

getInfCentRegTS(ErrorL2deriv, Regressor, neighbor, ...)
# S4 method for UnivariateDistribution,UnivariateDistribution,ContNeighborhood
getInfCentRegTS(
             ErrorL2deriv, Regressor, neighbor, clip, cent, stand, z.comp)
# S4 method for UnivariateDistribution,UnivariateDistribution,TotalVarNeighborhood
getInfCentRegTS(
             ErrorL2deriv, Regressor, neighbor, clip, cent, z.comp)
# S4 method for UnivariateDistribution,numeric,CondTotalVarNeighborhood
getInfCentRegTS(
             ErrorL2deriv, Regressor, neighbor, clip, cent, z.comp)
# S4 method for UnivariateDistribution,UnivariateDistribution,Av1CondContNeighborhood
getInfCentRegTS(
             ErrorL2deriv, Regressor, neighbor, clip, cent, stand, z.comp, x.vec)
# S4 method for UnivariateDistribution,UnivariateDistribution,Av1CondTotalVarNeighborhood
getInfCentRegTS(
             ErrorL2deriv, Regressor, neighbor, clip, cent, stand, z.comp, x.vec,
             tol.z)
# S4 method for UnivariateDistribution,MultivariateDistribution,ContNeighborhood
getInfCentRegTS(
             ErrorL2deriv, Regressor, neighbor, clip, cent, stand, z.comp)
# S4 method for UnivariateDistribution,MultivariateDistribution,Av1CondContNeighborhood
getInfCentRegTS(
             ErrorL2deriv, Regressor, neighbor, clip, cent, stand, z.comp, x.vec)
# S4 method for UnivariateDistribution,Distribution,Av2CondContNeighborhood
getInfCentRegTS(
             ErrorL2deriv, Regressor, neighbor, clip, cent, stand, z.comp, tol.z)
# S4 method for RealRandVariable,Distribution,ContNeighborhood
getInfCentRegTS(
             ErrorL2deriv, Regressor, neighbor, ErrorDistr, stand, cent, clip,
             z.comp)
# S4 method for RealRandVariable,Distribution,Av1CondContNeighborhood
getInfCentRegTS(
             ErrorL2deriv, Regressor, neighbor, ErrorDistr, stand, cent, clip,
             z.comp, x.vec)

Arguments

ErrorL2deriv

L2-derivative of ErrorDistr.

Regressor

regressor.

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.

x.vec

(approximated) support of Regressor.

tol.z

the desired accuracy (convergence tolerance).

ErrorDistr

error distribution.

Value

The optimal centering constant/function is computed.

Methods

ErrorL2deriv = "UnivariateDistribution", Regressor = "UnivariateDistribution", neighbor = "ContNeighborhood": computation of optimal centering constant.
ErrorL2deriv = "UnivariateDistribution", Regressor = "UnivariateDistribution", neighbor = "TotalVarNeighborhood": computation of lower clipping bound.
ErrorL2deriv = "UnivariateDistribution", Regressor = "numeric", neighbor = "CondTotalVarNeighborhood": computation of lower clipping bound.
ErrorL2deriv = "UnivariateDistribution", Regressor = "UnivariateDistribution", neighbor = "Av1CondContNeighborhood": computation of optimal centering function.
ErrorL2deriv = "UnivariateDistribution", Regressor = "UnivariateDistribution", neighbor = "Av1CondTotalVarNeighborhood": computation of optimal lower clipping function.
ErrorL2deriv = "UnivariateDistribution", Regressor = "MultivariateDistribution", neighbor = "ContNeighborhood": computation of optimal centering constant.
ErrorL2deriv = "UnivariateDistribution", Regressor = "MultivariateDistribution", neighbor = "Av1CondContNeighborhood": computation of optimal centering function.
ErrorL2deriv = "UnivariateDistribution", Regressor = "MultivariateDistribution", neighbor = "Av1CondTotalVarNeighborhood": computation of optimal lower clipping function.
ErrorL2deriv = "UnivariateDistribution", Regressor = "Distribution", neighbor = "Av2CondContNeighborhood": computation of optimal centering constant.
ErrorL2deriv = "RealRandVariable", Regressor = "Distribution", neighbor = "ContNeighborhood": computation of optimal centering constant.
ErrorL2deriv = "RealRandVariable", Regressor = "Distribution", neighbor = "Av1CondContNeighborhood": computation of optimal centering function.

References

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

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

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