getInfRobIC: Generic Function for the Computation of Optimally Robust ICs

In ROptEst: Optimally Robust Estimation

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, verbose = NULL)

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

## S4 method for signature 'RealRandVariable,asCov,UncondNeighborhood'
getInfRobIC(L2deriv, risk,
                       neighbor, Distr, Finfo, trafo, QuadForm = diag(nrow(trafo)),
                       verbose = NULL)

## S4 method for signature 'UnivariateDistribution,asBias,UncondNeighborhood'
getInfRobIC(L2deriv,
                       risk, neighbor, symm, trafo, maxiter, tol, warn, Finfo,
                       verbose = NULL, ...)

## S4 method for signature '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 signature '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 signature '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 signature 
## '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 signature '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 signature 'UnivariateDistribution,asGRisk,UncondNeighborhood'
getInfRobIC(L2deriv,
                       risk, neighbor, symm, Finfo, trafo, upper = NULL,
                       lower = NULL, maxiter, tol, warn, noLow = FALSE,
                       verbose = NULL, ...)

## S4 method for signature '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 signature 
## 'UnivariateDistribution,asUnOvShoot,UncondNeighborhood'
getInfRobIC(
                       L2deriv, risk, neighbor, symm, Finfo, trafo,
                       upper, lower, maxiter, tol, warn, verbose = NULL, ...)

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.

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 = "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(s)

Matthias Kohl [e-mail],
Peter Ruckdeschel [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.

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.

See Also

InfRobModel-class

ROptEst documentation built on Feb. 7, 2024, 3:02 p.m.