getAsRisk: Generic Function for Computation of Asymptotic Risks

Description

Generic function for the computation of asymptotic risks. This function is rarely called directly. It is used by other functions.

Usage

getAsRisk(risk, L2deriv, neighbor, ...)
# S4 method for asMSE,UnivariateDistribution,Neighborhood
getAsRisk(risk, L2deriv, neighbor, clip, cent, stand, trafo)
# S4 method for asMSE,EuclRandVariable,Neighborhood
getAsRisk(risk, L2deriv, neighbor, clip, cent, stand, trafo)
# S4 method for asBias,UnivariateDistribution,ContNeighborhood
getAsRisk(risk, L2deriv, neighbor, trafo)
# S4 method for asBias,UnivariateDistribution,TotalVarNeighborhood
getAsRisk(risk, L2deriv, neighbor, trafo)
# S4 method for asBias,RealRandVariable,ContNeighborhood
getAsRisk(risk, L2deriv, neighbor, Distr, L2derivDistrSymm, trafo, 
             z.start, A.start, maxiter, tol)
# S4 method for asCov,UnivariateDistribution,ContNeighborhood
getAsRisk(risk, L2deriv, neighbor, clip, cent, stand)
# S4 method for asCov,UnivariateDistribution,TotalVarNeighborhood
getAsRisk(risk, L2deriv, neighbor, clip, cent, stand)
# S4 method for asCov,RealRandVariable,ContNeighborhood
getAsRisk(risk, L2deriv, neighbor, Distr, clip, cent, stand)
# S4 method for trAsCov,UnivariateDistribution,UncondNeighborhood
getAsRisk(risk, L2deriv, neighbor, clip, cent, stand)
# S4 method for trAsCov,RealRandVariable,ContNeighborhood
getAsRisk(risk, L2deriv, neighbor, Distr, clip, cent, stand)
# S4 method for asUnOvShoot,UnivariateDistribution,UncondNeighborhood
getAsRisk(risk, L2deriv, neighbor, clip, cent, stand, trafo)

Arguments

risk

object of class "asRisk".

L2deriv

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

neighbor

object of class "Neighborhood".

…

additional parameters.

clip

optimal clipping bound.

cent

optimal centering constant.

stand

standardizing matrix.

trafo

matrix: transformation of the parameter.

Distr

object of class "Distribution".

L2derivDistrSymm

object of class "DistrSymmList".

z.start

initial value for the centering constant.

A.start

initial value for the standardizing matrix.

maxiter

the maximum number of iterations

tol

the desired accuracy (convergence tolerance).

Value

The asymptotic risk is computed.

Methods

risk = "asMSE", L2deriv = "UnivariateDistribution", neighbor = "Neighborhood":: computes asymptotic mean square error in methods for function getInfRobIC.
risk = "asMSE", L2deriv = "EuclRandVariable", neighbor = "Neighborhood":: computes asymptotic mean square error in methods for function getInfRobIC.
risk = "asBias", L2deriv = "UnivariateDistribution", neighbor = "ContNeighborhood":: computes standardized asymptotic bias in methods for function getInfRobIC.
risk = "asBias", L2deriv = "UnivariateDistribution", neighbor = "TotalVarNeighborhood":: computes standardized asymptotic bias in methods for function getInfRobIC.
risk = "asBias", L2deriv = "RealRandVariable", neighbor = "ContNeighborhood":: computes standardized asymptotic bias in methods for function getInfRobIC.
risk = "asCov", L2deriv = "UnivariateDistribution", neighbor = "ContNeighborhood":: computes asymptotic covariance in methods for function getInfRobIC.
risk = "asCov", L2deriv = "UnivariateDistribution", neighbor = "TotalVarNeighborhood":: computes asymptotic covariance in methods for function getInfRobIC.
risk = "asCov", L2deriv = "RealRandVariable", neighbor = "ContNeighborhood":: computes asymptotic covariance in methods for function getInfRobIC.
risk = "trAsCov", L2deriv = "UnivariateDistribution", neighbor = "UncondNeighborhood":: computes trace of asymptotic covariance in methods for function getInfRobIC.
risk = "trAsCov", L2deriv = "RealRandVariable", neighbor = "ContNeighborhood":: computes trace of asymptotic covariance in methods for function getInfRobIC.
risk = "asUnOvShoot", L2deriv = "UnivariateDistribution", neighbor = "UncondNeighborhood":: computes asymptotic under-/overshoot risk in methods for function getInfRobIC.

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Ruckdeschel, P. and Rieder, H. (2004) Optimal Influence Curves for General Loss Functions. Statistics & Decisions (submitted).