getInfRobIC: Generic Function for the Computation of Optimally Robust ICs In ROptEstOld: Optimally Robust Estimation - Old Version

Description

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

Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43``` ```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.

`InfRobModel-class`

ROptEstOld documentation built on May 2, 2019, 12:51 p.m.