Generic function for the computation of the radius minimax IC.
radiusMinimaxIC(L2Fam, neighbor, risk, ...)# S4 method for 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)
The radius minimax IC is computed.
L2-differentiable family of probability measures.
object of class "Neighborhood".
object of class "RiskType".
the lower end point of the interval to be searched in the inner optimization (for the least favorable situation to the user-guessed radius).
the upper end point of the interval to be searched in the inner optimization (for the least favorable situation to the user-guessed radius).
initial value for the centering constant.
initial value for the standardizing matrix.
upper bound for the optimal clipping bound.
lower bound for the optimal clipping bound.
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.
the maximum number of iterations
the desired accuracy (convergence tolerance).
logical: print warnings.
logical: if TRUE, some messages are printed
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
logical (of length 1):
if TRUE (not the default), in case of convergence problems in
the algorithm, returns NA.
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.
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.
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.
computation of the radius minimax IC for an L2 differentiable parametric family.
Matthias Kohl Matthias.Kohl@stamats.de, Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de
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.
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. 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 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. tools:::Rd_expr_doi("10.1524/stnd.22.3.201.57067")
radiusMinimaxIC
N <- NormLocationFamily(mean=0, sd=1)
radIC <- radiusMinimaxIC(L2Fam=N, neighbor=ContNeighborhood(),
risk=asMSE(), loRad=0.1, upRad=0.5)
checkIC(radIC)
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