# getInfRobIC: Generic Function for the Computation of Optimally Robust ICs In ROptEst: Optimally Robust Estimation

 getInfRobIC R Documentation

## 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 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.

InfRobModel-class