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

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

 ``` 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``` ```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 [email protected], Peter Ruckdeschel [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 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`