getInfRobRegTypeIC: Generic Function for the Computation of Optimally Robust Regression-Type ICs

Description

Generic function for the computation of optimally robust regression-type ICs in case of infinitesimal robust models. This function is rarely called directly.

Usage

getInfRobRegTypeIC(ErrorL2deriv, Regressor, risk, neighbor, ...)
# S4 method for UnivariateDistribution,UnivariateDistribution,asBias,ContNeighborhood
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorL2derivDistrSymm,
             RegSymm, Finfo, trafo, upper, maxiter, tol, warn)
# S4 method for UnivariateDistribution,UnivariateDistribution,asBias,Av1CondContNeighborhood
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorL2derivDistrSymm,
             RegSymm, Finfo, trafo, upper, maxiter, tol, warn)
# S4 method for UnivariateDistribution,UnivariateDistribution,asBias,Av1CondTotalVarNeighborhood
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorL2derivDistrSymm,
             RegSymm, Finfo, trafo, upper, maxiter, tol, warn)
# S4 method for UnivariateDistribution,Distribution,asBias,Av2CondContNeighborhood
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorL2derivDistrSymm,
             RegSymm, Finfo, trafo, upper, maxiter, tol, warn)
# S4 method for UnivariateDistribution,Distribution,asCov,ContNeighborhood
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorL2derivDistrSymm,
             RegSymm, Finfo, trafo)
# S4 method for UnivariateDistribution,UnivariateDistribution,asCov,TotalVarNeighborhood
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorL2derivDistrSymm,
             RegSymm, Finfo, trafo)
# S4 method for UnivariateDistribution,Distribution,asCov,CondContNeighborhood
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorL2derivDistrSymm,
             RegSymm, Finfo, trafo)
# S4 method for UnivariateDistribution,Distribution,asCov,CondTotalVarNeighborhood
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorL2derivDistrSymm,
             RegSymm, Finfo, trafo)
# S4 method for UnivariateDistribution,Distribution,asCov,Av1CondContNeighborhood
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorL2derivDistrSymm,
             RegSymm, Finfo, trafo)
# S4 method for UnivariateDistribution,Distribution,asCov,Av2CondContNeighborhood
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorL2derivDistrSymm,
             RegSymm, Finfo, trafo)
# S4 method for UnivariateDistribution,Distribution,asCov,Av1CondTotalVarNeighborhood
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorL2derivDistrSymm,
             RegSymm, Finfo, trafo)
# S4 method for UnivariateDistribution,Distribution,asGRisk,ContNeighborhood
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorL2derivDistrSymm,
             RegSymm, Finfo, trafo, upper, maxiter, tol, warn)
# S4 method for UnivariateDistribution,Distribution,asGRisk,Av1CondContNeighborhood
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorL2derivDistrSymm,
             RegSymm, Finfo, trafo, upper, maxiter, tol, warn)
# S4 method for UnivariateDistribution,Distribution,asGRisk,Av2CondContNeighborhood
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorL2derivDistrSymm,
             RegSymm, Finfo, trafo, upper, maxiter, tol, warn)
# S4 method for UnivariateDistribution,Distribution,asGRisk,Av1CondTotalVarNeighborhood
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorL2derivDistrSymm,
             RegSymm, Finfo, trafo, upper, maxiter, tol, warn)
# S4 method for UnivariateDistribution,MultivariateDistribution,asBias,ContNeighborhood
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorL2derivDistrSymm,
             RegSymm, Finfo, trafo, upper, maxiter, tol, warn)
# S4 method for UnivariateDistribution,MultivariateDistribution,asBias,Av1CondContNeighborhood
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorL2derivDistrSymm,
             RegSymm, Finfo, trafo, upper, maxiter, tol, warn)
# S4 method for UnivariateDistribution,MultivariateDistribution,asBias,Av1CondTotalVarNeighborhood
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorL2derivDistrSymm,
             RegSymm, Finfo, trafo, upper, maxiter, tol, warn)
# S4 method for RealRandVariable,Distribution,asBias,ContNeighborhood
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorSymm, RegSymm,
             ErrorDistr, ErrorL2derivSymm, ErrorL2derivDistrSymm, Finfo, trafo,
             upper, z.start, A.start, maxiter, tol, warn)
# S4 method for RealRandVariable,Distribution,asBias,Av1CondContNeighborhood
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorSymm, RegSymm,
             ErrorDistr, ErrorL2derivSymm, ErrorL2derivDistrSymm, Finfo, trafo,
             upper, z.start, A.start, maxiter, tol, warn)
# S4 method for RealRandVariable,Distribution,asCov,ContNeighborhood
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorDistr, Finfo, trafo)
# S4 method for RealRandVariable,Distribution,asCov,Av1CondContNeighborhood
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorDistr, Finfo, trafo)
# S4 method for RealRandVariable,Distribution,asGRisk,ContNeighborhood
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorSymm, RegSymm,
             ErrorDistr, ErrorL2derivSymm, ErrorL2derivDistrSymm, Finfo, trafo,
             upper, z.start, A.start, maxiter, tol, warn)
# S4 method for RealRandVariable,Distribution,asGRisk,Av1CondContNeighborhood
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorSymm, RegSymm,
             ErrorDistr, ErrorL2derivSymm, ErrorL2derivDistrSymm, Finfo, trafo,
             upper, z.start, A.start, maxiter, tol, warn)
# S4 method for UnivariateDistribution,UnivariateDistribution,asUnOvShoot,UncondNeighborhood
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorL2derivDistrSymm,
             RegSymm, Finfo, trafo, upper, maxiter, tol, warn)
# S4 method for UnivariateDistribution,UnivariateDistribution,asUnOvShoot,CondNeighborhood
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorL2derivDistrSymm,
             RegSymm, Finfo, trafo, upper, maxiter, tol, warn)

Arguments

ErrorL2deriv

L2-derivative of ErrorDistr.

Regressor

regressor.

risk

object of class "RiskType".

neighbor

object of class "Neighborhood".

…

additional parameters.

ErrorSymm

symmetry of ErrorDistr.

ErrorL2derivDistrSymm

symmetry of ErrorL2derivDistr.

RegSymm

symmetry of RegDistr.

ErrorDistr

error distribution.

ErrorL2derivSymm

symmetry of ErrorL2deriv.

Finfo

Fisher information matrix.

trafo

matrix: transformation of the parameter.

upper

upper bound for the optimal clipping bound.

maxiter

the maximum number of iterations

tol

the desired accuracy (convergence tolerance).

warn

logical: print warnings.

z.start

initial value for the centering constant/function.

A.start

initial value for the standardizing matrix.

Value

The optimally robust IC is computed.

Methods

ErrorL2deriv = "UnivariateDistribution", Regressor = "UnivariateDistribution", risk = "asBias", neighbor = "ContNeighborhood": computes the bias optimal influence curve for L2 differentiable regression-type families.
ErrorL2deriv = "UnivariateDistribution", Regressor = "UnivariateDistribution", risk = "asBias", neighbor = "Av1CondContNeighborhood": computes the bias optimal influence curve for L2 differentiable regression-type families.
ErrorL2deriv = "UnivariateDistribution", Regressor = "UnivariateDistribution", risk = "asBias", neighbor = "Av1CondTotalVarNeighborhood": computes the bias optimal influence curve for L2 differentiable regression-type families.
ErrorL2deriv = "UnivariateDistribution", Regressor = "Distribution", risk = "asBias", neighbor = "Av2CondContNeighborhood": computes the bias optimal influence curve for L2 differentiable regression-type families.
ErrorL2deriv = "UnivariateDistribution", Regressor = "Distribution", risk = "asCov", neighbor = "ContNeighborhood": computes the classical optimal influence curve for L2 differentiable regression-type families.
ErrorL2deriv = "UnivariateDistribution", Regressor = "UnivariateDistribution", risk = "asCov", neighbor = "TotalVarNeighborhood": computes the classical optimal influence curve for L2 differentiable regression-type families.
ErrorL2deriv = "UnivariateDistribution", Regressor = "Distribution", risk = "asCov", neighbor = "CondContNeighborhood": computes the classical optimal influence curve for L2 differentiable regression-type families.
ErrorL2deriv = "UnivariateDistribution", Regressor = "Distribution", risk = "asCov", neighbor = "CondTotalVarNeighborhood": computes the classical optimal influence curve for L2 differentiable regression-type families.
ErrorL2deriv = "UnivariateDistribution", Regressor = "Distribution", risk = "asCov", neighbor = "Av1CondContNeighborhood": computes the classical optimal influence curve for L2 differentiable regression-type families.
ErrorL2deriv = "UnivariateDistribution", Regressor = "Distribution", risk = "asCov", neighbor = "Av2CondContNeighborhood": computes the classical optimal influence curve for L2 differentiable regression-type families.
ErrorL2deriv = "UnivariateDistribution", Regressor = "Distribution", risk = "asCov", neighbor = "Av1CondTotalVarNeighborhood": computes the classical optimal influence curve for L2 differentiable regression-type families.
ErrorL2deriv = "UnivariateDistribution", Regressor = "Distribution", risk = "asGRisk", neighbor = "ContNeighborhood": computes the optimally robust influence curve for L2 differentiable regression-type families.
ErrorL2deriv = "UnivariateDistribution", Regressor = "Distribution", risk = "asGRisk", neighbor = "Av1CondContNeighborhood": computes the optimally robust influence curve for L2 differentiable regression-type families.
ErrorL2deriv = "UnivariateDistribution", Regressor = "Distribution", risk = "asGRisk", neighbor = "Av2CondContNeighborhood": computes the optimally robust influence curve for L2 differentiable regression-type families.
ErrorL2deriv = "UnivariateDistribution", Regressor = "Distribution", risk = "asGRisk", neighbor = "Av1CondTotalVarNeighborhood": computes the optimally robust influence curve for L2 differentiable regression-type families.
ErrorL2deriv = "UnivariateDistribution", Regressor = "MultivariateDistribution", risk = "asBias", neighbor = "ContNeighborhood": computes the bias optimal influence curve for L2 differentiable regression-type families.
ErrorL2deriv = "UnivariateDistribution", Regressor = "MultivariateDistribution", risk = "asBias", neighbor = "Av1CondContNeighborhood": computes the bias optimal influence curve for L2 differentiable regression-type families.
ErrorL2deriv = "UnivariateDistribution", Regressor = "MultivariateDistribution", risk = "asBias", neighbor = "Av1CondTotalVarNeighborhood": computes the bias optimal influence curve for L2 differentiable regression-type families.
ErrorL2deriv = "RealRandVariable", Regressor = "Distribution", risk = "asBias", neighbor = "ContNeighborhood": computes the bias optimal influence curve for L2 differentiable regression-type families.
ErrorL2deriv = "RealRandVariable", Regressor = "Distribution", risk = "asCov", neighbor = "ContNeighborhood": computes the classical optimal influence curve for L2 differentiable regression-type families.
ErrorL2deriv = "RealRandVariable", Regressor = "Distribution", risk = "asCov", neighbor = "Av1CondContNeighborhood": computes the classical optimal influence curve for L2 differentiable regression-type families.
ErrorL2deriv = "RealRandVariable", Regressor = "Distribution", risk = "asGRisk", neighbor = "ContNeighborhood": computes the optimally robust influence curve for L2 differentiable regression-type families.
ErrorL2deriv = "RealRandVariable", Regressor = "Distribution", risk = "asGRisk", neighbor = "Av1CondContNeighborhood": computes the optimally robust influence curve for L2 differentiable regression-type families.
ErrorL2deriv = "UnivariateDistribution", Regressor = "UnivariateDistribution", risk = "asUnOvShoot", neighbor = "UncondNeighborhood": computes the optimally robust influence curve for L2 differentiable regression-type families.
ErrorL2deriv = "UnivariateDistribution", Regressor = "UnivariateDistribution", risk = "asUnOvShoot", neighbor = "CondNeighborhood": computes the optimally robust influence curve for L2 differentiable regression-type families.

References

Rieder, H. (1980) Estimates derived from robust tests. Ann. Stats. 8: 106--115.

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