getInfV: Generic Function for the Computation of the asymptotic...

In ROptEst: Optimally Robust Estimation

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

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.

Value

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

Author(s)

Peter Ruckdeschel [e-mail]

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.

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.