getInfCent: Generic Function for the Computation of the Optimal Centering...

In ROptEst: Optimally Robust Estimation

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 signature 'UnivariateDistribution,ContNeighborhood,BiasType'
getInfCent(L2deriv, 
     neighbor, biastype, clip, cent, tol.z, symm, trafo)

## S4 method for signature 
## 'UnivariateDistribution,TotalVarNeighborhood,BiasType'
getInfCent(L2deriv, 
     neighbor, biastype, clip, cent, tol.z, symm, trafo)

## S4 method for signature 'RealRandVariable,ContNeighborhood,BiasType'
getInfCent(L2deriv,
     neighbor, biastype, Distr, z.comp, w, tol.z = .Machine$double.eps^.5, ...)

## S4 method for signature 'RealRandVariable,TotalVarNeighborhood,BiasType'
getInfCent(L2deriv,
     neighbor, biastype, Distr, z.comp, w, tol.z = .Machine$double.eps^.5,...)

## S4 method for signature 
## 'UnivariateDistribution,ContNeighborhood,onesidedBias'
getInfCent(L2deriv,
     neighbor, biastype, clip, cent, tol.z, symm, trafo)

## S4 method for signature 
## 'UnivariateDistribution,ContNeighborhood,asymmetricBias'
getInfCent(L2deriv, 
     neighbor, biastype, clip, cent, tol.z, symm, trafo)

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.

Value

The optimal centering constant is computed.

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(s)

Matthias Kohl [e-mail], Peter Ruckdeschel [e-mail]

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.

See Also

ContIC-class, TotalVarIC-class

ROptEst documentation built on Sept. 12, 2024, 7:40 a.m.