Generic Function for the Computation of the Optimal Clipping Bound
Generic Function for the Computation of the Optimal Clipping Bound
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.
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).
Returns
The optimal clipping height is computed. More specifically, the optimal clipping height b is determined in a zero search of a certain function gamma, where the respective getInf-method will return the value of gamma(b). The actual function gamma
varies according to whether the parameter is one dimensional or higher dimensional, according to the risk, according to the neighborhood, and according to the bias type, which leads to the different methods.
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.
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.