getInfRobIC: Generic Function for the Computation of Optimally Robust ICs

In ROptEstOld: Optimally Robust Estimation - Old Version

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 signature 'UnivariateDistribution,asCov,ContNeighborhood'
getInfRobIC(L2deriv, risk, neighbor, Finfo, trafo)

## S4 method for signature 'UnivariateDistribution,asCov,TotalVarNeighborhood'
getInfRobIC(L2deriv, risk, neighbor, Finfo, trafo)

## S4 method for signature 'RealRandVariable,asCov,ContNeighborhood'
getInfRobIC(L2deriv, risk, neighbor, Distr, Finfo, trafo)

## S4 method for signature 'UnivariateDistribution,asBias,ContNeighborhood'
getInfRobIC(L2deriv, risk, neighbor, symm, Finfo, trafo, 
             upper, maxiter, tol, warn)

## S4 method for signature 'UnivariateDistribution,asBias,TotalVarNeighborhood'
getInfRobIC(L2deriv, risk, neighbor, symm, Finfo, trafo, 
             upper, maxiter, tol, warn)

## S4 method for signature 'RealRandVariable,asBias,ContNeighborhood'
getInfRobIC(L2deriv, risk, neighbor, Distr, DistrSymm, L2derivSymm, 
             L2derivDistrSymm, Finfo, z.start, A.start, trafo, upper, maxiter, tol, warn)

## S4 method for signature 'UnivariateDistribution,asHampel,UncondNeighborhood'
getInfRobIC(L2deriv, risk, neighbor, symm, Finfo, trafo, 
             upper, maxiter, tol, warn)

## S4 method for signature 'RealRandVariable,asHampel,ContNeighborhood'
getInfRobIC(L2deriv, risk, neighbor, Distr, DistrSymm, L2derivSymm, 
             L2derivDistrSymm, Finfo, trafo, z.start, A.start, upper, maxiter, tol, warn)

## S4 method for signature 'UnivariateDistribution,asGRisk,UncondNeighborhood'
getInfRobIC(L2deriv, risk, neighbor, symm, Finfo, trafo, 
             upper, maxiter, tol, warn)

## S4 method for signature 'RealRandVariable,asGRisk,ContNeighborhood'
getInfRobIC(L2deriv, risk, neighbor, Distr, DistrSymm, L2derivSymm, 
             L2derivDistrSymm, Finfo, trafo, z.start, A.start, upper, maxiter, tol, warn)

## S4 method for signature 
## '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.

Author(s)

Matthias Kohl [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.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

InfRobModel-class

ROptEstOld documentation built on Feb. 4, 2024, 3 p.m.