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, verbose = NULL)
# S4 method for UnivariateDistribution,asCov,TotalVarNeighborhood
getInfRobIC(L2deriv,
                       risk, neighbor, Finfo, trafo, verbose = NULL)
# S4 method for RealRandVariable,asCov,UncondNeighborhood
getInfRobIC(L2deriv, risk,
                       neighbor, Distr, Finfo, trafo, QuadForm = diag(nrow(trafo)),
                       verbose = NULL)
# S4 method for UnivariateDistribution,asBias,UncondNeighborhood
getInfRobIC(L2deriv,
                       risk, neighbor, symm, trafo, maxiter, tol, warn, Finfo,
                       verbose = NULL, ...)
# S4 method for RealRandVariable,asBias,UncondNeighborhood
getInfRobIC(L2deriv, risk,
                       neighbor, Distr, DistrSymm, L2derivSymm,
                       L2derivDistrSymm, z.start, A.start, Finfo, trafo,
                       maxiter, tol, warn, verbose = NULL, ...)
# S4 method for UnivariateDistribution,asHampel,UncondNeighborhood
getInfRobIC(L2deriv,
                       risk, neighbor, symm, Finfo, trafo, upper = NULL,
                       lower=NULL, maxiter, tol, warn, noLow = FALSE,
                       verbose = NULL, checkBounds = TRUE, ...)
# S4 method for RealRandVariable,asHampel,UncondNeighborhood
getInfRobIC(L2deriv, risk,
                       neighbor, Distr, DistrSymm, L2derivSymm,
                       L2derivDistrSymm, Finfo, trafo, onesetLM = FALSE,
                       z.start, A.start, upper = NULL, lower=NULL,
                       OptOrIter = "iterate", maxiter, tol, warn,
                       verbose = NULL, checkBounds = TRUE, ...,
                       .withEvalAsVar = TRUE)
# S4 method for UnivariateDistribution,asAnscombe,UncondNeighborhood
getInfRobIC(
                       L2deriv, risk, neighbor, symm, Finfo, trafo, upper = NULL,
                       lower=NULL, maxiter, tol, warn, noLow = FALSE,
                       verbose = NULL, checkBounds = TRUE, ...)
# S4 method for RealRandVariable,asAnscombe,UncondNeighborhood
getInfRobIC(L2deriv, 
                       risk, neighbor, Distr, DistrSymm, L2derivSymm,
                       L2derivDistrSymm, Finfo, trafo, onesetLM = FALSE,
                       z.start, A.start, upper = NULL, lower=NULL,
                       OptOrIter = "iterate", maxiter, tol, warn,
                       verbose = NULL, checkBounds = TRUE, ...)
# S4 method for UnivariateDistribution,asGRisk,UncondNeighborhood
getInfRobIC(L2deriv,
                       risk, neighbor, symm, Finfo, trafo, upper = NULL,
                       lower = NULL, maxiter, tol, warn, noLow = FALSE,
                       verbose = NULL, ...)
# S4 method for RealRandVariable,asGRisk,UncondNeighborhood
getInfRobIC(L2deriv, risk,
                       neighbor,  Distr, DistrSymm, L2derivSymm,
                       L2derivDistrSymm, Finfo, trafo, onesetLM = FALSE, z.start,
                       A.start, upper = NULL, lower = NULL, OptOrIter = "iterate",
                       maxiter, tol, warn, verbose = NULL, withPICcheck = TRUE,
                       ..., .withEvalAsVar = TRUE)
# S4 method for UnivariateDistribution,asUnOvShoot,UncondNeighborhood
getInfRobIC(
                       L2deriv, risk, neighbor, symm, Finfo, trafo,
                       upper, lower, maxiter, tol, warn, verbose = NULL, ...)

Value

The optimally robust IC is computed.

Arguments

L2deriv: L2-derivative of some L2-differentiable family of probability measures.
risk: object of class "RiskType".
neighbor: object of class "Neighborhood".
...: additional parameters (mainly for optim).
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.
lower: lower bound for the optimal clipping bound.
OptOrIter: character; which method to be used for determining Lagrange multipliers A and a: if (partially) matched to "optimize", getLagrangeMultByOptim is used; otherwise: by default, or if matched to "iterate" or to "doubleiterate", getLagrangeMultByIter is used. More specifically, when using getLagrangeMultByIter, and if argument risk is of class "asGRisk", by default and if matched to "iterate" we use only one (inner) iteration, if matched to "doubleiterate" we use up to Maxiter (inner) iterations.
maxiter: the maximum number of iterations.
tol: the desired accuracy (convergence tolerance).
warn: logical: print warnings.
noLow: logical: is lower case to be computed?
onesetLM: logical: use one set of Lagrange multipliers?
QuadForm: matrix of (or which may coerced to) class PosSemDefSymmMatrix for use of different (standardizing) norm
verbose: logical: if TRUE, some messages are printed
checkBounds: logical: if TRUE, minimal and maximal clipping bound are computed to check if a valid bound was specified.
withPICcheck: logical: at the end of the algorithm, shall we check how accurately this is a pIC; this will only be done if withPICcheck && verbose.
.withEvalAsVar: logical (of length 1): if TRUE, risks based on covariances are to be evaluated (default), otherwise just a call is returned.

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 = "UncondNeighborhood": computes the classical optimal influence curve for L2 differentiable parametric families with unknown \(k\)-dimensional parameter (\(k > 1\)) where the underlying distribution is univariate; for total variation neighborhoods only is implemented for the case where there is a \(1\times k\) transformation trafo matrix.
L2deriv = "UnivariateDistribution", risk = "asBias", neighbor = "UncondNeighborhood": computes the bias optimal influence curve for L2 differentiable parametric families with unknown one-dimensional parameter.
L2deriv = "RealRandVariable", risk = "asBias", neighbor = "UncondNeighborhood": 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 = "UncondNeighborhood": computes the optimally robust influence curve for L2 differentiable parametric families with unknown \(k\)-dimensional parameter (\(k > 1\)) where the underlying distribution is univariate; for total variation neighborhoods only is implemented for the case where there is a \(1\times k\) transformation trafo matrix.
L2deriv = "UnivariateDistribution", risk = "asAnscombe", neighbor = "UncondNeighborhood": computes the optimally bias-robust influence curve to given ARE in the ideal model for L2 differentiable parametric families with unknown one-dimensional parameter.
L2deriv = "RealRandVariable", risk = "asAnscombe", neighbor = "UncondNeighborhood": computes the optimally bias-robust influence curve to given ARE in the ideal modelfor L2 differentiable parametric families with unknown \(k\)-dimensional parameter (\(k > 1\)) where the underlying distribution is univariate; for total variation neighborhoods only is implemented for the case where there is a \(1\times k\) transformation trafo matrix.
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 = "UncondNeighborhood": computes the optimally robust influence curve for L2 differentiable parametric families with unknown \(k\)-dimensional parameter (\(k > 1\)) where the underlying distribution is univariate; for total variation neighborhoods only is implemented for the case where there is a \(1\times k\) transformation trafo matrix.
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

Matthias Kohl Matthias.Kohl@stamats.de,
Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

References

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

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

Ruckdeschel, P. and Rieder, H. (2004) Optimal Influence Curves for General Loss Functions. Statistics & Decisions 22: 201-223.

Ruckdeschel, P. (2005) Optimally One-Sided Bounded Influence Curves. Mathematical Methods in Statistics 14(1), 105-131.

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