leastFavorableRadius: Generic Function for the Computation of Least Favorable Radii

Description

Generic function for the computation of least favorable radii.

Usage

leastFavorableRadius(L2Fam, neighbor, risk, ...)
# S4 method for L2ParamFamily,UncondNeighborhood,asGRisk
leastFavorableRadius(
          L2Fam, neighbor, risk, rho, upRad = 1, 
            z.start = NULL, A.start = NULL, upper = 100,
            OptOrIter = "iterate", maxiter = 100,
            tol = .Machine$double.eps^0.4, warn = FALSE, verbose = NULL, ...)

Value

The least favorable radius and the corresponding inefficiency are computed.

Arguments

L2Fam: L2-differentiable family of probability measures.
neighbor: object of class "Neighborhood".
risk: object of class "RiskType".
upRad: the upper end point of the radius interval to be searched.
rho: The considered radius interval is: \([r \rho, r/\rho]\) with \(\rho\in(0,1)\).
z.start: initial value for the centering constant.
A.start: initial value for the standardizing matrix.
upper: upper 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
...: additional arguments to be passed to E

Methods

L2Fam = "L2ParamFamily", neighbor = "UncondNeighborhood", risk = "asGRisk": computation of the least favorable radius.

Author

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

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. 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")

Examples

Run this code

N <- NormLocationFamily(mean=0, sd=1) 
leastFavorableRadius(L2Fam=N, neighbor=ContNeighborhood(),
                     risk=asMSE(), rho=0.5)

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