getInfCent: Generic Function for the Computation of the Optimal Centering Constant/Lower Clipping Bound

Description

Generic function for the computation of the optimal centering constant (contamination neighborhoods) respectively, of the optimal lower clipping bound (total variation neighborhood). This function is rarely called directly. It is used to compute optimally robust ICs.

Usage

getInfCent(L2deriv, neighbor, biastype, ...)
# S4 method for UnivariateDistribution,ContNeighborhood,BiasType
getInfCent(L2deriv, 
     neighbor, biastype, clip, cent, tol.z, symm, trafo)
# S4 method for UnivariateDistribution,TotalVarNeighborhood,BiasType
getInfCent(L2deriv, 
     neighbor, biastype, clip, cent, tol.z, symm, trafo)
# S4 method for RealRandVariable,ContNeighborhood,BiasType
getInfCent(L2deriv,
     neighbor, biastype, Distr, z.comp, w, tol.z = .Machine$double.eps^.5, ...)
# S4 method for RealRandVariable,TotalVarNeighborhood,BiasType
getInfCent(L2deriv,
     neighbor, biastype, Distr, z.comp, w, tol.z = .Machine$double.eps^.5,...)
# S4 method for UnivariateDistribution,ContNeighborhood,onesidedBias
getInfCent(L2deriv,
     neighbor, biastype, clip, cent, tol.z, symm, trafo)
# S4 method for UnivariateDistribution,ContNeighborhood,asymmetricBias
getInfCent(L2deriv, 
     neighbor, biastype, clip, cent, tol.z, symm, trafo)

Value

The optimal centering constant 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: optimal clipping bound.
cent: optimal centering constant.
tol.z: the desired accuracy (convergence tolerance).
symm: logical: indicating symmetry of L2deriv.
trafo: matrix: transformation of the parameter.
Distr: object of class Distribution.
z.comp: logical vector: indication which components of the centering constant have to be computed.
w: object of class RobWeight; current weight.

Methods

L2deriv = "UnivariateDistribution", neighbor = "ContNeighborhood", biastype = "BiasType": computation of optimal centering constant for symmetric bias.
L2deriv = "UnivariateDistribution", neighbor = "TotalVarNeighborhood", biastype = "BiasType": computation of optimal lower clipping bound for symmetric bias.
L2deriv = "RealRandVariable", neighbor = "TotalVarNeighborhood", biastype = "BiasType": computation of optimal centering constant for symmetric bias.
L2deriv = "RealRandVariable", neighbor = "ContNeighborhood", biastype = "BiasType": computation of optimal centering constant for symmetric bias.
L2deriv = "UnivariateDistribution", neighbor = "ContNeighborhood", biastype = "onesidedBias": computation of optimal centering constant for onesided bias.
L2deriv = "UnivariateDistribution", neighbor = "ContNeighborhood", biastype = "asymmetricBias": computation of optimal centering constant for asymmetric bias.

Author

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

References

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.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.