# getInfGammaRegTS: Generic Function for the Computation of the Optimal Clipping... In ROptRegTS: Optimally robust estimation for regression-type models

## Description

Generic function for the computation of the optimal clipping bound. This function is rarely called directly. It is called by `getInfClipRegTS` 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 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89``` ```getInfGammaRegTS(ErrorL2deriv, Regressor, risk, neighbor, ...) ## S4 method for signature ## 'UnivariateDistribution,UnivariateDistribution,asMSE,ContNeighborhood' getInfGammaRegTS( ErrorL2deriv, Regressor, risk, neighbor, z.comp, stand, cent, clip) ## S4 method for signature ## 'UnivariateDistribution, ## UnivariateDistribution, ## asMSE, ## Av1CondContNeighborhood' getInfGammaRegTS( ErrorL2deriv, Regressor, risk, neighbor, z.comp, stand, cent, clip) ## S4 method for signature ## 'UnivariateDistribution, ## UnivariateDistribution, ## asMSE, ## Av1CondTotalVarNeighborhood' getInfGammaRegTS( ErrorL2deriv, Regressor, risk, neighbor, z.comp, stand, cent, clip) ## S4 method for signature ## 'UnivariateDistribution, ## MultivariateDistribution, ## asMSE, ## ContNeighborhood' getInfGammaRegTS( ErrorL2deriv, Regressor, risk, neighbor, z.comp, stand, cent, clip) ## S4 method for signature ## 'UnivariateDistribution, ## MultivariateDistribution, ## asMSE, ## Av1CondContNeighborhood' getInfGammaRegTS( ErrorL2deriv, Regressor, risk, neighbor, z.comp, stand, cent, clip) ## S4 method for signature ## 'UnivariateDistribution, ## MultivariateDistribution, ## asMSE, ## Av1CondTotalVarNeighborhood' getInfGammaRegTS( ErrorL2deriv, Regressor, risk, neighbor, z.comp, stand, cent, clip) ## S4 method for signature ## 'UnivariateDistribution,Distribution,asMSE,Av2CondContNeighborhood' getInfGammaRegTS( ErrorL2deriv, Regressor, risk, neighbor, z.comp, stand, cent, clip) ## S4 method for signature ## 'RealRandVariable,Distribution,asMSE,ContNeighborhood' getInfGammaRegTS( ErrorL2deriv, Regressor, risk, neighbor, ErrorDistr, stand, cent, clip) ## S4 method for signature ## 'RealRandVariable,Distribution,asMSE,Av1CondContNeighborhood' getInfGammaRegTS( ErrorL2deriv, Regressor, risk, neighbor, ErrorDistr, stand, cent, clip) ## S4 method for signature ## 'UnivariateDistribution, ## UnivariateDistribution, ## asUnOvShoot, ## ContNeighborhood' getInfGammaRegTS( ErrorL2deriv, Regressor, risk, neighbor, cent, clip) ## S4 method for signature ## 'UnivariateDistribution, ## UnivariateDistribution, ## asUnOvShoot, ## TotalVarNeighborhood' getInfGammaRegTS( ErrorL2deriv, Regressor, risk, neighbor, cent, clip) ## S4 method for signature ## 'UnivariateDistribution,numeric,asUnOvShoot,CondContNeighborhood' getInfGammaRegTS( ErrorL2deriv, Regressor, risk, neighbor, clip) ## S4 method for signature ## 'UnivariateDistribution,numeric,asUnOvShoot,CondTotalVarNeighborhood' getInfGammaRegTS( ErrorL2deriv, Regressor, risk, neighbor, clip) ```

## Arguments

 `ErrorL2deriv` L2-derivative of `ErrorDistr`. `Regressor` regressor. `risk` object of class `"RiskType"`. `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. `ErrorDistr` error distribution.

## Details

The function is used in case of asymptotic G-risks; confer Ruckdeschel and Rieder (2004).

## Methods

ErrorL2deriv = "UnivariateDistribution", Regressor = "UnivariateDistribution", risk = "asMSE", neighbor = "ContNeighborhood"

used by `getInfClipRegTS`.

ErrorL2deriv = "UnivariateDistribution", Regressor = "UnivariateDistribution", risk = "asMSE", neighbor = "Av1CondContNeighborhood"

used by `getInfClipRegTS`.

ErrorL2deriv = "UnivariateDistribution", Regressor = "UnivariateDistribution", risk = "asMSE", neighbor = "Av1CondTotalVarNeighborhood"

used by `getInfClipRegTS`.

ErrorL2deriv = "UnivariateDistribution", Regressor = "MultivariateDistribution", risk = "asMSE", neighbor = "ContNeighborhood"

used by `getInfClipRegTS`.

ErrorL2deriv = "UnivariateDistribution", Regressor = "MultivariateDistribution", risk = "asMSE", neighbor = "Av1CondContNeighborhood"

used by `getInfClipRegTS`.

ErrorL2deriv = "UnivariateDistribution", Regressor = "MultivariateDistribution", risk = "asMSE", neighbor = "Av1CondTotalVarNeighborhood"

used by `getInfClipRegTS`.

ErrorL2deriv = "UnivariateDistribution", Regressor = "Distribution", risk = "asMSE", neighbor = "Av2CondContNeighborhood"

used by `getInfClipRegTS`.

ErrorL2deriv = "RealRandVariable", Regressor = "Distribution", risk = "asMSE", neighbor = "ContNeighborhood"

used by `getInfClipRegTS`.

ErrorL2deriv = "RealRandVariable", Regressor = "Distribution", risk = "asMSE", neighbor = "Av1CondContNeighborhood"

used by `getInfClipRegTS`.

ErrorL2deriv = "UnivariateDistribution", Regressor = "UnivariateDistribution", risk = "asUnOvShoot", neighbor = "ContNeighborhood"

used by `getInfClipRegTS`.

ErrorL2deriv = "UnivariateDistribution", Regressor = "UnivariateDistribution", risk = "asUnOvShoot", neighbor = "TotalVarNeighborhood"

used by `getInfClipRegTS`.

ErrorL2deriv = "UnivariateDistribution", Regressor = "numeric", risk = "asUnOvShoot", neighbor = "CondContNeighborhood"

used by `getInfClipRegTS`.

ErrorL2deriv = "UnivariateDistribution", Regressor = "numeric", risk = "asUnOvShoot", neighbor = "CondTotalVarNeighborhood"

used by `getInfClipRegTS`.

## Author(s)

Matthias Kohl [email protected]

## References

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

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

Ruckdeschel, P. and Rieder, H. (2004) Optimal Influence Curves for General Loss Functions. Statistics & Decisions (submitted).

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

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