# getInfCentRegTS: Generic Function for the Computation of the Optimal Centering... In ROptRegTS: Optimally Robust Estimation for Regression-Type Models

## 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

 ``` 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 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59``` ```getInfCentRegTS(ErrorL2deriv, Regressor, neighbor, ...) ## S4 method for signature ## 'UnivariateDistribution,UnivariateDistribution,ContNeighborhood' getInfCentRegTS( ErrorL2deriv, Regressor, neighbor, clip, cent, stand, z.comp) ## S4 method for signature ## 'UnivariateDistribution,UnivariateDistribution,TotalVarNeighborhood' getInfCentRegTS( ErrorL2deriv, Regressor, neighbor, clip, cent, z.comp) ## S4 method for signature ## 'UnivariateDistribution,numeric,CondTotalVarNeighborhood' getInfCentRegTS( ErrorL2deriv, Regressor, neighbor, clip, cent, z.comp) ## S4 method for signature ## 'UnivariateDistribution, ## UnivariateDistribution, ## Av1CondContNeighborhood' getInfCentRegTS( ErrorL2deriv, Regressor, neighbor, clip, cent, stand, z.comp, x.vec) ## S4 method for signature ## 'UnivariateDistribution, ## UnivariateDistribution, ## Av1CondTotalVarNeighborhood' getInfCentRegTS( ErrorL2deriv, Regressor, neighbor, clip, cent, stand, z.comp, x.vec, tol.z) ## S4 method for signature ## 'UnivariateDistribution,MultivariateDistribution,ContNeighborhood' getInfCentRegTS( ErrorL2deriv, Regressor, neighbor, clip, cent, stand, z.comp) ## S4 method for signature ## 'UnivariateDistribution, ## MultivariateDistribution, ## Av1CondContNeighborhood' getInfCentRegTS( ErrorL2deriv, Regressor, neighbor, clip, cent, stand, z.comp, x.vec) ## S4 method for signature ## 'UnivariateDistribution,Distribution,Av2CondContNeighborhood' getInfCentRegTS( ErrorL2deriv, Regressor, neighbor, clip, cent, stand, z.comp, tol.z) ## S4 method for signature 'RealRandVariable,Distribution,ContNeighborhood' getInfCentRegTS( ErrorL2deriv, Regressor, neighbor, ErrorDistr, stand, cent, clip, z.comp) ## S4 method for signature ## '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.

## Author(s)

Matthias Kohl Matthias.Kohl@stamats.de

## 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.

`ContIC-class`, `Av1CondContIC-class`, `Av2CondContIC-class`, `Av1CondTotalVarIC-class`, `CondContIC-class`, `CondTotalVarIC-class`