# getInfGamma: Generic Function for the Computation of the Optimal Clipping... In ROptEst: Optimally Robust Estimation

 getInfGamma R Documentation

## Generic Function for the Computation of the Optimal Clipping Bound

### Description

Generic function for the computation of the optimal clipping bound. This function is rarely called directly. It is called by `getInfClip` to compute optimally robust ICs.

### Usage

```getInfGamma(L2deriv, risk, neighbor, biastype, ...)

## S4 method for signature
## 'UnivariateDistribution,asGRisk,ContNeighborhood,BiasType'
getInfGamma(L2deriv,
risk, neighbor, biastype, cent, clip)

## S4 method for signature
## 'UnivariateDistribution,asGRisk,TotalVarNeighborhood,BiasType'
getInfGamma(L2deriv,
risk, neighbor, biastype, cent, clip)

## S4 method for signature 'RealRandVariable,asMSE,ContNeighborhood,BiasType'
getInfGamma(L2deriv,
risk, neighbor, biastype, Distr, stand, cent, clip, power = 1L, ...)

## S4 method for signature
## 'RealRandVariable,asMSE,TotalVarNeighborhood,BiasType'
getInfGamma(L2deriv,
risk, neighbor, biastype, Distr, stand, cent, clip, power = 1L, ...)

## S4 method for signature
## 'UnivariateDistribution,asUnOvShoot,ContNeighborhood,BiasType'
getInfGamma(L2deriv,
risk, neighbor, biastype, cent, clip)

## S4 method for signature
## 'UnivariateDistribution,asMSE,ContNeighborhood,onesidedBias'
getInfGamma(L2deriv,
risk, neighbor, biastype, cent, clip)

## S4 method for signature
## 'UnivariateDistribution,asMSE,ContNeighborhood,asymmetricBias'
getInfGamma(L2deriv,
risk, neighbor, biastype, cent, clip)
```

### Arguments

 `L2deriv` L2-derivative of some L2-differentiable family of probability measures. `risk` object of class `"RiskType"`. `neighbor` object of class `"Neighborhood"`. `biastype` object of class `"BiasType"`. `...` additional parameters, in particular for expectation `E`. `cent` optimal centering constant. `clip` optimal clipping bound. `stand` standardizing matrix. `Distr` object of class `"Distribution"`. `power` exponent for the integrand; by default `1`, but may also be `2`, for optimization in `getLagrangeMultByOptim`.

### Details

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

### Methods

L2deriv = "UnivariateDistribution", risk = "asGRisk", neighbor = "ContNeighborhood", biastype = "BiasType"

used by `getInfClip` for symmetric bias.

L2deriv = "UnivariateDistribution", risk = "asGRisk", neighbor = "TotalVarNeighborhood", biastype = "BiasType"

used by `getInfClip` for symmetric bias.

L2deriv = "RealRandVariable", risk = "asMSE", neighbor = "ContNeighborhood", biastype = "BiasType"

used by `getInfClip` for symmetric bias.

L2deriv = "RealRandVariable", risk = "asMSE", neighbor = "TotalVarNeighborhood", biastype = "BiasType"

used by `getInfClip` for symmetric bias.

L2deriv = "UnivariateDistribution", risk = "asUnOvShoot", neighbor = "ContNeighborhood", biastype = "BiasType"

used by `getInfClip` for symmetric bias.

L2deriv = "UnivariateDistribution", risk = "asMSE", neighbor = "ContNeighborhood", biastype = "onesidedBias"

used by `getInfClip` for onesided bias.

L2deriv = "UnivariateDistribution", risk = "asMSE", neighbor = "ContNeighborhood", biastype = "asymmetricBias"

used by `getInfClip` for asymmetric bias.

### Author(s)

Matthias Kohl Matthias.Kohl@stamats.de, Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

### 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 22, 201-223.

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.

`asGRisk-class`, `asMSE-class`, `asUnOvShoot-class`, `ContIC-class`, `TotalVarIC-class`