ROptEstOld: getInfRobIC – R documentation

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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 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 Matthias.Kohl@stamats.de

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.