# getInfCent: Generic Function for the Computation of the Optimal Centering... In ROptEst: Optimally Robust Estimation

## 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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28``` ```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.

`ContIC-class`, `TotalVarIC-class`