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

In ROptEst: Optimally Robust Estimation

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 [e-mail], Peter Ruckdeschel [e-mail]

References

M. Kohl (2005). Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation. https://epub.uni-bayreuth.de/id/eprint/839/2/DissMKohl.pdf.

H. Rieder, M. Kohl, and P. Ruckdeschel (2008). The Costs of not Knowing the Radius. Statistical Methods and Applications, 17(1) 13-40. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s10260-007-0047-7")}.

H. Rieder, M. Kohl, and P. Ruckdeschel (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 \Sexpr[results=rd]{tools:::Rd_expr_doi("10.18452/3638")}.

P. Ruckdeschel (2005). Optimally One-Sided Bounded Influence Curves. Mathematical Methods of Statistics 14(1), 105-131.

P. Ruckdeschel and H. Rieder (2004). Optimal Influence Curves for General Loss Functions. Statistics & Decisions 22, 201-223. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1524/stnd.22.3.201.57067")}

See Also

radiusMinimaxIC

Examples

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 Sept. 12, 2024, 7:40 a.m.