getInfCent {ROptEst}R Documentation

Generic Function for the Computation of the Optimal Centering Constant/Lower Clipping Bound

Description

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

Usage

getInfCent(L2deriv, neighbor, biastype, ...)

## S4 method for signature 'UnivariateDistribution,
##   ContNeighborhood, BiasType':
getInfCent(L2deriv, 
     neighbor, biastype, clip, cent, tol.z, symm, trafo)

## S4 method for signature 'UnivariateDistribution,
##   TotalVarNeighborhood, BiasType':
getInfCent(L2deriv, 
     neighbor, biastype, clip, cent, tol.z, symm, trafo)

## S4 method for signature 'RealRandVariable,
##   ContNeighborhood, BiasType':
getInfCent(L2deriv, 
     neighbor, biastype, Distr, z.comp, w)

## S4 method for signature 'UnivariateDistribution,
##   ContNeighborhood, onesidedBias':
getInfCent(L2deriv, 
     neighbor, biastype, clip, cent, tol.z, symm, trafo)

## S4 method for signature 'UnivariateDistribution,
##   ContNeighborhood, asymmetricBias':
getInfCent(L2deriv, 
     neighbor, biastype, clip, cent, tol.z, symm, 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.
clip optimal clipping bound.
cent optimal centering constant.
tol.z the desired accuracy (convergence tolerance).
symm logical: indicating symmetry of L2deriv.
trafo matrix: transformation of the parameter.
Distr object of class Distribution.
z.comp logical vector: indication which components of the centering constant have to be computed.
w object of class RobWeight; current weight

Value

The optimal centering constant is computed.

Methods

L2deriv = "UnivariateDistribution", neighbor = "ContNeighborhood", biastype = "BiasType"
computation of optimal centering constant for symmetric bias.
L2deriv = "UnivariateDistribution", neighbor = "TotalVarNeighborhood", biastype = "BiasType"
computation of optimal lower clipping bound for symmetric bias.
L2deriv = "RealRandVariable", neighbor = "ContNeighborhood", biastype = "BiasType"
computation of optimal centering constant for symmetric bias.
L2deriv = "UnivariateDistribution", neighbor = "ContNeighborhood", biastype = "onesidedBias"
computation of optimal centering constant for onesided bias.
L2deriv = "UnivariateDistribution", neighbor = "ContNeighborhood", biastype = "asymmetricBias"
computation of optimal centering constant for asymmetric bias.

Author(s)

Matthias Kohl Matthias.Kohl@stamats.de, Peter Ruckdeschel Peter.Ruckdeschel@itwm.fraunhofer.de

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


[Package ROptEst version 0.6.3 Index]