ROptEst: getInfGamma – R documentation

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getInfGamma

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.