radiusMinimaxIC: Generic function for the computation of the radius minimax IC

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

Description

Generic function for the computation of the radius minimax IC.

Usage

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radiusMinimaxIC(L2Fam, neighbor, risk, ...)

## S4 method for signature 'L2ParamFamily,UncondNeighborhood,asGRisk'
radiusMinimaxIC(
        L2Fam, neighbor, risk, loRad = 0, upRad = Inf, z.start = NULL, A.start = NULL, 
        upper = NULL, lower = NULL, OptOrIter = "iterate",
        maxiter = 50, tol = .Machine$double.eps^0.4,
        warn = FALSE, verbose = NULL, loRad0 = 1e-3, ...,
        returnNAifProblem = FALSE, loRad.s = NULL, upRad.s = NULL,
        modifyICwarn = NULL)

Arguments

L2Fam

L2-differentiable family of probability measures.

neighbor

object of class "Neighborhood".

risk

object of class "RiskType".

loRad

the lower end point of the interval to be searched in the inner optimization (for the least favorable situation to the user-guessed radius).

upRad

the upper end point of the interval to be searched in the inner optimization (for the least favorable situation to the user-guessed radius).

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.

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.

verbose

logical: if TRUE, some messages are printed

loRad0

for numerical reasons: the effective lower bound for the zero search; internally set to max(loRad,loRad0).

...

further arguments to be passed on to getInfRobIC

returnNAifProblem

logical (of length 1): if TRUE (not the default), in case of convergence problems in the algorithm, returns NA.

loRad.s

the lower end point of the interval to be searched in the outer optimization (for the user-guessed radius); if NULL (default) set to loRad in the algorithm.

upRad.s

the upper end point of the interval to be searched in the outer optimization (for the user-guessed radius); if NULL (default) set to upRad in the algorithm.

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 the neighborhood radius is unknown, Rieder et al. (2001, 2008) and Kohl (2005) show that there is nevertheless a way to compute an optimally robust IC - the so-called radius-minimax IC - which is optimal for some radius interval.

Value

The radius minimax IC is computed.

Methods

L2Fam = "L2ParamFamily", neighbor = "UncondNeighborhood", risk = "asGRisk":

computation of the radius minimax IC for an L2 differentiable parametric family.

Author(s)

Matthias Kohl [email protected], Peter Ruckdeschel [email protected]

References

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 www.uni-bayreuth.de/departments/math/org/mathe7/RIEDER/pubs/RR.pdf

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

See Also

radiusMinimaxIC

Examples

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N <- NormLocationFamily(mean=0, sd=1) 
radIC <- radiusMinimaxIC(L2Fam=N, neighbor=ContNeighborhood(), 
                         risk=asMSE(), loRad=0.1, upRad=0.5)
checkIC(radIC)

ROptEst documentation built on May 2, 2019, 5:45 p.m.