getInfV: Generic Function for the Computation of the asymptotic Variance of a Hampel type IC

Description

Generic function for the computation of the optimal clipping bound in case of infinitesimal robust models. This function is rarely called directly. It is used to compute optimally robust ICs.

Usage

getInfV(L2deriv, neighbor, biastype, ...)
# S4 method for UnivariateDistribution,ContNeighborhood,BiasType
getInfV(L2deriv, 
         neighbor, biastype, clip, cent, stand)
# S4 method for UnivariateDistribution,TotalVarNeighborhood,BiasType
getInfV(L2deriv, 
         neighbor, biastype, clip, cent, stand)
# S4 method for RealRandVariable,ContNeighborhood,BiasType
getInfV(L2deriv, 
         neighbor, biastype, Distr, V.comp, cent, stand, 
         w, ...)
# S4 method for RealRandVariable,TotalVarNeighborhood,BiasType
getInfV(L2deriv,
         neighbor, biastype, Distr, V.comp, cent, stand,
         w, ...)
# S4 method for UnivariateDistribution,ContNeighborhood,onesidedBias
getInfV(L2deriv,
         neighbor, biastype, clip, cent, stand, ...)
# S4 method for UnivariateDistribution,ContNeighborhood,asymmetricBias
getInfV(L2deriv, 
         neighbor, biastype, clip, cent, stand)

Value

The asymptotic variance of an ALE to IC of Hampel type is computed.

Arguments

L2deriv: L2-derivative of some L2-differentiable family of probability measures.
neighbor: object of class "Neighborhood".
biastype: object of class "BiasType".
...: additional parameters, in particular for expectation E.
clip: positive real: clipping bound
cent: optimal centering constant.
stand: standardizing matrix.
Distr: standardizing matrix.
V.comp: matrix: indication which components of the standardizing matrix have to be computed.
w: object of class RobWeight; current weight.

Author

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. (2005) Optimally One-Sided Bounded Influence Curves. Mathematical Methods in Statistics 14(1), 105-131.