getInfClip: Generic Function for the Computation of the Optimal Clipping...

In ROptEst: Optimally Robust Estimation

Generic Function for the Computation of the Optimal Clipping Bound

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

getInfClip(clip, L2deriv, risk, neighbor, ...)

## S4 method for signature 
## 'numeric,UnivariateDistribution,asMSE,ContNeighborhood'
getInfClip(
     clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo)

## S4 method for signature 
## 'numeric,UnivariateDistribution,asMSE,TotalVarNeighborhood'
getInfClip(
     clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo)

## S4 method for signature 
## 'numeric,UnivariateDistribution,asL1,ContNeighborhood'
getInfClip(
     clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo)

## S4 method for signature 
## 'numeric,UnivariateDistribution,asL1,TotalVarNeighborhood'
getInfClip(
     clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo)

## S4 method for signature 
## 'numeric,UnivariateDistribution,asL4,ContNeighborhood'
getInfClip(
     clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo)

## S4 method for signature 
## 'numeric,UnivariateDistribution,asL4,TotalVarNeighborhood'
getInfClip(
     clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo)

## S4 method for signature 'numeric,EuclRandVariable,asMSE,UncondNeighborhood'
getInfClip(
     clip, L2deriv, risk, neighbor, biastype, Distr, stand, cent, trafo, ...)

## S4 method for signature 
## 'numeric,UnivariateDistribution,asUnOvShoot,UncondNeighborhood'
getInfClip(
     clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo)

## S4 method for signature 
## 'numeric,UnivariateDistribution,asSemivar,ContNeighborhood'
getInfClip(
     clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo,...)

Arguments

clip	positive real: clipping bound
L2deriv	L2-derivative of some L2-differentiable family of probability measures.
risk	object of class "RiskType".
neighbor	object of class "Neighborhood".
...	additional parameters, in particular for expectation E
biastype	object of class "BiasType"
cent	optimal centering constant.
stand	standardizing matrix.
Distr	object of class "Distribution".
symm	logical: indicating symmetry of L2deriv.
trafo	matrix: transformation of the parameter.

Value

The optimal clipping bound is computed.

Methods

clip = "numeric", L2deriv = "UnivariateDistribution", risk = "asMSE", neighbor = "ContNeighborhood"

optimal clipping bound for asymtotic mean square error.

clip = "numeric", L2deriv = "UnivariateDistribution", risk = "asMSE", neighbor = "TotalVarNeighborhood"

optimal clipping bound for asymtotic mean square error.

clip = "numeric", L2deriv = "EuclRandVariable", risk = "asMSE", neighbor = "UncondNeighborhood"

optimal clipping bound for asymtotic mean square error.

clip = "numeric", L2deriv = "UnivariateDistribution", risk = "asL1", neighbor = "ContNeighborhood"

optimal clipping bound for asymtotic mean absolute error.

clip = "numeric", L2deriv = "UnivariateDistribution", risk = "asL1", neighbor = "TotalVarNeighborhood"

optimal clipping bound for asymtotic mean absolute error.

clip = "numeric", L2deriv = "UnivariateDistribution", risk = "asL4", neighbor = "ContNeighborhood"

optimal clipping bound for asymtotic mean power 4 error.

clip = "numeric", L2deriv = "UnivariateDistribution", risk = "asL4", neighbor = "TotalVarNeighborhood"

optimal clipping bound for asymtotic mean power 4 error.

clip = "numeric", L2deriv = "UnivariateDistribution", risk = "asUnOvShoot", neighbor = "UncondNeighborhood"

optimal clipping bound for asymtotic under-/overshoot risk.

clip = "numeric", L2deriv = "UnivariateDistribution", risk = "asSemivar", neighbor = "ContNeighborhood"

optimal clipping bound for asymtotic semivariance.

Author(s)

Matthias Kohl [e-mail], 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. 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.

See Also

ContIC-class, TotalVarIC-class

ROptEst documentation built on Nov. 17, 2022, 1:06 a.m.