getInfRobIC: Generic Function for the Computation of Optimally Robust ICs

Description Usage Arguments Value Methods Author(s) References See Also

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
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
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 x 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 x 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 x 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 x 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 [email protected],
Peter Ruckdeschel [email protected]

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 May 2, 2019, 5:45 p.m.