getAsRiskRegTS: Generic Function for Computation of Asymptotic Risks in case of Regression-Type Models

Description

Generic function for the computation of asymptotic risks in case of regression-type models. This function is rarely called directly. It is used by other functions.

Usage

getAsRiskRegTS(risk, ErrorL2deriv, Regressor, neighbor, ...)
# S4 method for asMSE,UnivariateDistribution,Distribution,Neighborhood
getAsRiskRegTS(
             risk, ErrorL2deriv, Regressor, neighbor, clip, cent, stand, trafo)
# S4 method for asMSE,UnivariateDistribution,Distribution,Av2CondContNeighborhood
getAsRiskRegTS(
             risk, ErrorL2deriv, Regressor, neighbor, clip, cent, stand, trafo)
# S4 method for asMSE,EuclRandVariable,Distribution,Neighborhood
getAsRiskRegTS(
             risk, ErrorL2deriv, Regressor, neighbor, clip, cent, stand, trafo)
# S4 method for asBias,UnivariateDistribution,UnivariateDistribution,ContNeighborhood
getAsRiskRegTS(
             risk, ErrorL2deriv, Regressor, neighbor, ErrorL2derivDistrSymm,
             trafo, maxiter, tol)
# S4 method for asBias,UnivariateDistribution,UnivariateDistribution,Av1CondContNeighborhood
getAsRiskRegTS(
             risk, ErrorL2deriv, Regressor, neighbor, ErrorL2derivDistrSymm,
             trafo, maxiter, tol)
# S4 method for asBias,UnivariateDistribution,UnivariateDistribution,Av1CondTotalVarNeighborhood
getAsRiskRegTS(
             risk, ErrorL2deriv, Regressor, neighbor, ErrorL2derivDistrSymm,
             trafo, maxiter, tol)
# S4 method for asBias,UnivariateDistribution,MultivariateDistribution,ContNeighborhood
getAsRiskRegTS(
             risk, ErrorL2deriv, Regressor, neighbor, ErrorL2derivDistrSymm,
             trafo, maxiter, tol)
# S4 method for asBias,UnivariateDistribution,MultivariateDistribution,Av1CondContNeighborhood
getAsRiskRegTS(
             risk, ErrorL2deriv, Regressor, neighbor, ErrorL2derivDistrSymm,
             trafo, maxiter, tol)
# S4 method for asBias,UnivariateDistribution,MultivariateDistribution,Av1CondTotalVarNeighborhood
getAsRiskRegTS(
             risk, ErrorL2deriv, Regressor, neighbor, ErrorL2derivDistrSymm,
             trafo, maxiter, tol)
# S4 method for asBias,UnivariateDistribution,Distribution,Av2CondContNeighborhood
getAsRiskRegTS(
             risk, ErrorL2deriv, Regressor, neighbor, ErrorL2derivDistrSymm,
             trafo, maxiter, tol)
# S4 method for asBias,RealRandVariable,Distribution,ContNeighborhood
getAsRiskRegTS(
             risk, ErrorL2deriv, Regressor, neighbor, ErrorDistr, trafo, z.start,
             A.start, maxiter, tol)
# S4 method for asBias,RealRandVariable,Distribution,Av1CondContNeighborhood
getAsRiskRegTS(
             risk, ErrorL2deriv, Regressor, neighbor, ErrorDistr, trafo, z.start,
             A.start, maxiter, tol)
# S4 method for asUnOvShoot,UnivariateDistribution,UnivariateDistribution,UncondNeighborhood
getAsRiskRegTS(
             risk, ErrorL2deriv, Regressor, neighbor, clip, cent, stand)
# S4 method for asUnOvShoot,UnivariateDistribution,UnivariateDistribution,CondNeighborhood
getAsRiskRegTS(
             risk, ErrorL2deriv, Regressor, neighbor, clip, cent, stand)

Arguments

risk

object of class "asRisk".

ErrorL2deriv

L2-derivative of ErrorDistr.

Regressor

regressor.

neighbor

object of class "Neighborhood".

…

additional parameters.

clip

optimal clipping bound.

cent

optimal centering constant/function.

stand

standardizing matrix.

trafo

matrix: transformation of the parameter.

ErrorDistr

error distribution.

ErrorL2derivDistrSymm

symmetry of ErrorL2derivDistr.

maxiter

the maximum number of iterations

tol

the desired accuracy (convergence tolerance).

z.start

initial value for the centering constant/function.

A.start

initial value for the standardizing matrix.

Value

The asymptotic risk is computed.

Methods

risk = "asMSE", ErrorL2deriv = "UnivariateDistribution", Regressor = "Distribution", neighbor = "Neighborhood": computes asymptotic mean square error in methods for function getInfRobRegTypeIC.
risk = "asMSE", ErrorL2deriv = "UnivariateDistribution", Regressor = "Distribution", neighbor = "Av2CondContNeighborhood": computes asymptotic mean square error in methods for function getInfRobRegTypeIC.
risk = "asMSE", ErrorL2deriv = "EuclRandVariable", Regressor = "Distribution", neighbor = "Neighborhood": computes asymptotic mean square error in methods for function getInfRobRegTypeIC.
risk = "asBias", ErrorL2deriv = "UnivariateDistribution", Regressor = "UnivariateDistribution", neighbor = "ContNeighborhood": computes standardized asymptotic bias in methods for function getInfRobRegTypeIC.
risk = "asBias", ErrorL2deriv = "UnivariateDistribution", Regressor = "UnivariateDistribution", neighbor = "Av1CondContNeighborhood": computes standardized asymptotic bias in methods for function getInfRobRegTypeIC.
risk = "asBias", ErrorL2deriv = "UnivariateDistribution", Regressor = "UnivariateDistribution", neighbor = "Av1CondTotalVarNeighborhood": computes standardized asymptotic bias in methods for function getInfRobRegTypeIC.
risk = "asBias", ErrorL2deriv = "UnivariateDistribution", Regressor = "MultivariateDistribution", neighbor = "ContNeighborhood": computes standardized asymptotic bias in methods for function getInfRobRegTypeIC.
risk = "asBias", ErrorL2deriv = "UnivariateDistribution", Regressor = "MultivariateDistribution", neighbor = "Av1CondContNeighborhood": computes standardized asymptotic bias in methods for function getInfRobRegTypeIC.
risk = "asBias", ErrorL2deriv = "UnivariateDistribution", Regressor = "MultivariateDistribution", neighbor = "Av1CondTotalVarNeighborhood": computes standardized asymptotic bias in methods for function getInfRobRegTypeIC.
risk = "asBias", ErrorL2deriv = "UnivariateDistribution", Regressor = "Distribution", neighbor = "Av2CondContNeighborhood": computes standardized asymptotic bias in methods for function getInfRobRegTypeIC.
risk = "asBias", ErrorL2deriv = "RealRandVariable", Regressor = "Distribution", neighbor = "ContNeighborhood": computes standardized asymptotic bias in methods for function getInfRobRegTypeIC.
risk = "asBias", ErrorL2deriv = "RealRandVariable", Regressor = "Distribution", neighbor = "Av1CondContNeighborhood": computes standardized asymptotic bias in methods for function getInfRobRegTypeIC.
risk = "asUnOvShoot", ErrorL2deriv = "UnivariateDistribution", Regressor = "UnivariateDistribution", neighbor = "UncondNeighborhood": computes asymptotic under-/overshoot risk in methods for function getInfRobRegTypeIC.
risk = "asUnOvShoot", ErrorL2deriv = "UnivariateDistribution", Regressor = "UnivariateDistribution", neighbor = "CondNeighborhood": computes asymptotic under-/overshoot risk in methods for function getInfRobRegTypeIC.

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 (submitted).