getInfRad: Generic Function for the Computation of the Optimal Radius...

In ROptEst: Optimally Robust Estimation

Generic Function for the Computation of the Optimal Radius for Given Clipping Bound

Description

The usual robust optimality problem for given asGRisk searches the optimal clipping height b of a Hampel-type IC to given radius of the neighborhood. Instead, again for given asGRisk and for given Hampel-Type IC with given clipping height b we may determine the radius of the neighborhood for which it is optimal in the sense of the first sentence. This radius is determined by getInfRad. This function is rarely called directly. It is used withing getRadius.

Usage

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

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

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

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

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

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

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

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

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

## S4 method for signature 
## 'numeric,UnivariateDistribution,asSemivar,ContNeighborhood'
getInfRad(
          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.
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)

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 Sept. 12, 2024, 7:40 a.m.