ROptEst: radiusMinimaxIC – R documentation

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ROptEst

radiusMinimaxIC

Generic function for the computation of the radius minimax IC

Description

Generic function for the computation of the radius minimax IC.

Usage

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 Matthias.Kohl@stamats.de, Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

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.

Examples

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

ROptEst

Optimally Robust Estimation

v1.2.1

LGPL-3

Authors

Matthias Kohl [cre, cph], Mykhailo Pupashenko [ctb] (contributed wrapper functions for diagnostic plots), Gerald Kroisandt [ctb] (contributed testing routines), Peter Ruckdeschel [aut, cph]

Initial release

2019-04-07

radiusMinimaxIC

Description

Usage

Arguments

Details

Value

Methods

Author(s)

References

See Also

Examples

ROptEst

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