optIC: 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.

Usage

optIC(model, risk, ...)

## S4 method for signature 'InfRobModel,asRisk'
optIC(model, risk, z.start = NULL, A.start = NULL,
                                     upper = 1e4, lower = 1e-4,
                                     OptOrIter = "iterate", maxiter = 50,
                                     tol = .Machine$double.eps^0.4, warn = TRUE, 
                                     noLow = FALSE, verbose = NULL, ...,
                                     .withEvalAsVar = TRUE, withMakeIC = FALSE,
                                     returnNAifProblem = FALSE, modifyICwarn = NULL)

## S4 method for signature 'InfRobModel,asUnOvShoot'
optIC(model, risk, upper = 1e4,
                                          lower = 1e-4, maxiter = 50,
                                          tol = .Machine$double.eps^0.4,
                                          withMakeIC = FALSE, warn = TRUE,
                                          verbose = NULL, modifyICwarn = NULL, ...)

## S4 method for signature 'FixRobModel,fiUnOvShoot'
optIC(model, risk, sampleSize, upper = 1e4, lower = 1e-4,
                                          maxiter = 50, tol = .Machine$double.eps^0.4, 
                                          withMakeIC = FALSE, warn = TRUE,
                                          Algo = "A", cont = "left",
                                          verbose = NULL, modifyICwarn = NULL, ...)

Arguments

model	probability model.
risk	object of class "RiskType".
...	additional arguments; e.g. are passed on to E via e.g. makeIC in case of all signature, and, in addition, to getInfRobIC in case of signature("InfRobModel","asRisk").
z.start	initial value for the centering constant.
A.start	initial value for the standardizing matrix.
upper	upper bound for the optimal clipping bound.
lower	lower bound for the optimal clipping bound.
maxiter	the maximum number of iterations.
tol	the desired accuracy (convergence tolerance).
warn	logical: print warnings.
sampleSize	integer: sample size.
Algo	"A" or "B".
cont	"left" or "right".
noLow	logical: is lower case to be computed?
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.
verbose	logical: if TRUE, some messages are printed.
.withEvalAsVar	logical (of length 1): if TRUE, risks based on covariances are to be evaluated (default), otherwise just a call is returned.
withMakeIC	logical; if TRUE the [p]IC is passed through makeIC before return.
returnNAifProblem	logical (of length 1): if TRUE (not the default), in case of convergence problems in the algorithm, returns NA.
modifyICwarn	logical: should a (warning) information be added if modifyIC is applied and hence some optimality information could no longer be valid? Defaults to NULL in which case this value is taken from RobAStBaseOptions.

Details

In case of the finite-sample risk "fiUnOvShoot" one can choose between two algorithms for the computation of this risk where the least favorable contamination is assumed to be left or right of some bound. For more details we refer to Section 11.3 of Kohl (2005).

Value

Some optimally robust IC is computed.

Methods

model = "InfRobModel", risk = "asRisk"

computes optimally robust influence curve for robust models with infinitesimal neighborhoods and various asymptotic risks.

model = "InfRobModel", risk = "asUnOvShoot"

computes optimally robust influence curve for robust models with infinitesimal neighborhoods and asymptotic under-/overshoot risk.

model = "FixRobModel", risk = "fiUnOvShoot"

computes optimally robust influence curve for robust models with fixed neighborhoods and finite-sample under-/overshoot risk.

Author(s)

Matthias Kohl [e-mail]

References

Huber, P.J. (1968) Robust Confidence Limits. Z. Wahrscheinlichkeitstheor. Verw. Geb. 10:269–278.

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

Kohl, M. and Ruckdeschel, P. (2010): R package distrMod: Object-Oriented Implementation of Probability Models. J. Statist. Softw. 35(10), 1–27

Kohl, M. and Ruckdeschel, P., and Rieder, H. (2010): Infinitesimally Robust Estimation in General Smoothly Parametrized Models. Stat. Methods Appl., 19, 333–354.

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

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

Rieder, H., Kohl, M. and Ruckdeschel, P. (2008) The Costs of not Knowing the Radius. Statistical Methods and Applications 17(1) 13-40.

Rieder, H., Kohl, M. and Ruckdeschel, P. (2001) The Costs of not Knowing the Radius. Appeared as discussion paper Nr. 81. SFB 373 (Quantification and Simulation of Economic Processes), Humboldt University, Berlin; also available under doi: 10.18452/3638

See Also

InfluenceCurve-class, RiskType-class

Examples

B <- BinomFamily(size = 25, prob = 0.25) 

## classical optimal IC
IC0 <- optIC(model = B, risk = asCov())
plot(IC0) # plot IC
checkIC(IC0, B)

ROptEst documentation built on Nov. 17, 2022, 1:06 a.m.