getInfCent: Generic Function for the Computation of the Optimal Centering...

Description Usage Arguments Value Methods Author(s) References See Also

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

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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, tol.z = .Machine$double.eps^.5, ...)

## S4 method for signature 'RealRandVariable,TotalVarNeighborhood,BiasType'
getInfCent(L2deriv,
     neighbor, biastype, Distr, z.comp, w, tol.z = .Machine$double.eps^.5,...)

## 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, in particular for expectation E.

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 = "TotalVarNeighborhood", biastype = "BiasType"

computation of optimal centering constant 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@uni-oldenburg.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


ROptEst documentation built on May 2, 2019, 3:42 a.m.

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