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

Description Usage Arguments Details Methods Author(s) References See Also

Description

Generic function for the computation of the optimal clipping bound. This function is rarely called directly. It is called by getInfClip to compute optimally robust ICs.

Usage

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getInfGamma(L2deriv, risk, neighbor, biastype, ...)

## S4 method for signature 
## 'UnivariateDistribution,asGRisk,ContNeighborhood,BiasType'
getInfGamma(L2deriv, 
     risk, neighbor, biastype, cent, clip)

## S4 method for signature 
## 'UnivariateDistribution,asGRisk,TotalVarNeighborhood,BiasType'
getInfGamma(L2deriv, 
     risk, neighbor, biastype, cent, clip)

## S4 method for signature 'RealRandVariable,asMSE,ContNeighborhood,BiasType'
getInfGamma(L2deriv, 
     risk, neighbor, biastype, Distr, stand, cent, clip, power = 1L, ...)

## S4 method for signature 
## 'RealRandVariable,asMSE,TotalVarNeighborhood,BiasType'
getInfGamma(L2deriv,
     risk, neighbor, biastype, Distr, stand, cent, clip, power = 1L, ...)

## S4 method for signature 
## 'UnivariateDistribution,asUnOvShoot,ContNeighborhood,BiasType'
getInfGamma(L2deriv,
     risk, neighbor, biastype, cent, clip)

## S4 method for signature 
## 'UnivariateDistribution,asMSE,ContNeighborhood,onesidedBias'
getInfGamma(L2deriv, 
     risk, neighbor, biastype, cent, clip)

## S4 method for signature 
## 'UnivariateDistribution,asMSE,ContNeighborhood,asymmetricBias'
getInfGamma(L2deriv, 
    risk, neighbor, biastype, cent, clip)

Arguments

L2deriv

L2-derivative of some L2-differentiable family of probability measures.

risk

object of class "RiskType".

neighbor

object of class "Neighborhood".

biastype

object of class "BiasType".

...

additional parameters, in particular for expectation E.

cent

optimal centering constant.

clip

optimal clipping bound.

stand

standardizing matrix.

Distr

object of class "Distribution".

power

exponent for the integrand; by default 1, but may also be 2, for optimization in getLagrangeMultByOptim.

Details

The function is used in case of asymptotic G-risks; confer Ruckdeschel and Rieder (2004).

Methods

L2deriv = "UnivariateDistribution", risk = "asGRisk", neighbor = "ContNeighborhood", biastype = "BiasType"

used by getInfClip for symmetric bias.

L2deriv = "UnivariateDistribution", risk = "asGRisk", neighbor = "TotalVarNeighborhood", biastype = "BiasType"

used by getInfClip for symmetric bias.

L2deriv = "RealRandVariable", risk = "asMSE", neighbor = "ContNeighborhood", biastype = "BiasType"

used by getInfClip for symmetric bias.

L2deriv = "RealRandVariable", risk = "asMSE", neighbor = "TotalVarNeighborhood", biastype = "BiasType"

used by getInfClip for symmetric bias.

L2deriv = "UnivariateDistribution", risk = "asUnOvShoot", neighbor = "ContNeighborhood", biastype = "BiasType"

used by getInfClip for symmetric bias.

L2deriv = "UnivariateDistribution", risk = "asMSE", neighbor = "ContNeighborhood", biastype = "onesidedBias"

used by getInfClip for onesided bias.

L2deriv = "UnivariateDistribution", risk = "asMSE", neighbor = "ContNeighborhood", biastype = "asymmetricBias"

used by getInfClip for asymmetric bias.

Author(s)

Matthias Kohl [email protected], Peter Ruckdeschel [email protected]

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

asGRisk-class, asMSE-class, asUnOvShoot-class, ContIC-class, TotalVarIC-class


ROptEst documentation built on May 2, 2019, 5:45 p.m.