getInfRobIC: Generic Function for the Computation of Optimally Robust ICs

Description

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

Usage

getInfRobIC(L2deriv, risk, neighbor, ...)
# S4 method for UnivariateDistribution,asCov,ContNeighborhood
getInfRobIC(L2deriv, risk, neighbor, Finfo, trafo)
# S4 method for UnivariateDistribution,asCov,TotalVarNeighborhood
getInfRobIC(L2deriv, risk, neighbor, Finfo, trafo)
# S4 method for RealRandVariable,asCov,ContNeighborhood
getInfRobIC(L2deriv, risk, neighbor, Distr, Finfo, trafo)
# S4 method for UnivariateDistribution,asBias,ContNeighborhood
getInfRobIC(L2deriv, risk, neighbor, symm, Finfo, trafo, 
             upper, maxiter, tol, warn)
# S4 method for UnivariateDistribution,asBias,TotalVarNeighborhood
getInfRobIC(L2deriv, risk, neighbor, symm, Finfo, trafo, 
             upper, maxiter, tol, warn)
# S4 method for RealRandVariable,asBias,ContNeighborhood
getInfRobIC(L2deriv, risk, neighbor, Distr, DistrSymm, L2derivSymm, 
             L2derivDistrSymm, Finfo, z.start, A.start, trafo, upper, maxiter, tol, warn)
# S4 method for UnivariateDistribution,asHampel,UncondNeighborhood
getInfRobIC(L2deriv, risk, neighbor, symm, Finfo, trafo, 
             upper, maxiter, tol, warn)
# S4 method for RealRandVariable,asHampel,ContNeighborhood
getInfRobIC(L2deriv, risk, neighbor, Distr, DistrSymm, L2derivSymm, 
             L2derivDistrSymm, Finfo, trafo, z.start, A.start, upper, maxiter, tol, warn)
# S4 method for UnivariateDistribution,asGRisk,UncondNeighborhood
getInfRobIC(L2deriv, risk, neighbor, symm, Finfo, trafo, 
             upper, maxiter, tol, warn)
# S4 method for RealRandVariable,asGRisk,ContNeighborhood
getInfRobIC(L2deriv, risk, neighbor, Distr, DistrSymm, L2derivSymm, 
             L2derivDistrSymm, Finfo, trafo, z.start, A.start, upper, maxiter, tol, warn)
# S4 method for UnivariateDistribution,asUnOvShoot,UncondNeighborhood
getInfRobIC(L2deriv, risk, neighbor, symm, Finfo, trafo, 
             upper, maxiter, tol, warn)

Arguments

L2deriv

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

risk

object of class "RiskType".

neighbor

object of class "Neighborhood".

…

additional parameters.

Distr

object of class "Distribution".

symm

logical: indicating symmetry of L2deriv.

DistrSymm

object of class "DistributionSymmetry".

L2derivSymm

object of class "FunSymmList".

L2derivDistrSymm

object of class "DistrSymmList".

Finfo

Fisher information matrix.

z.start

initial value for the centering constant.

A.start

initial value for the standardizing 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.

Value

The optimally robust IC is computed.

Methods

L2deriv = "UnivariateDistribution", risk = "asCov", neighbor = "ContNeighborhood": computes the classical optimal influence curve for L2 differentiable parametric families with unknown one-dimensional parameter.
L2deriv = "UnivariateDistribution", risk = "asCov", neighbor = "TotalVarNeighborhood": computes the classical optimal influence curve for L2 differentiable parametric families with unknown one-dimensional parameter.
L2deriv = "RealRandVariable", risk = "asCov", neighbor = "ContNeighborhood": computes the classical optimal influence curve for L2 differentiable parametric families with unknown \(k\)-dimensional parameter (\(k > 1\)) where the underlying distribution is univariate.
L2deriv = "UnivariateDistribution", risk = "asBias", neighbor = "ContNeighborhood": computes the bias optimal influence curve for L2 differentiable parametric families with unknown one-dimensional parameter.
L2deriv = "UnivariateDistribution", risk = "asBias", neighbor = "TotalVarNeighborhood": computes the bias optimal influence curve for L2 differentiable parametric families with unknown one-dimensional parameter.
L2deriv = "RealRandVariable", risk = "asBias", neighbor = "ContNeighborhood": computes the bias optimal influence curve for L2 differentiable parametric families with unknown \(k\)-dimensional parameter (\(k > 1\)) where the underlying distribution is univariate.
L2deriv = "UnivariateDistribution", risk = "asHampel", neighbor = "UncondNeighborhood": computes the optimally robust influence curve for L2 differentiable parametric families with unknown one-dimensional parameter.
L2deriv = "RealRandVariable", risk = "asHampel", neighbor = "ContNeighborhood": computes the optimally robust influence curve for L2 differentiable parametric families with unknown \(k\)-dimensional parameter (\(k > 1\)) where the underlying distribution is univariate.
L2deriv = "UnivariateDistribution", risk = "asGRisk", neighbor = "UncondNeighborhood": computes the optimally robust influence curve for L2 differentiable parametric families with unknown one-dimensional parameter.
L2deriv = "RealRandVariable", risk = "asGRisk", neighbor = "ContNeighborhood": computes the optimally robust influence curve for L2 differentiable parametric families with unknown \(k\)-dimensional parameter (\(k > 1\)) where the underlying distribution is univariate.
L2deriv = "UnivariateDistribution", risk = "asUnOvShoot", neighbor = "UncondNeighborhood": computes the optimally robust influence curve for one-dimensional L2 differentiable parametric families and asymptotic under-/overshoot risk.

References

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

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