leastFavorableRadius: Generic Function for the Computation of Least Favorable Radii

In ROptEst: Optimally Robust Estimation

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 signature '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, ...)

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

Value

The least favorable radius and the corresponding inefficiency are computed.

Methods

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

computation of the least favorable radius.

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) 
leastFavorableRadius(L2Fam=N, neighbor=ContNeighborhood(),
                     risk=asMSE(), rho=0.5)

ROptEst documentation built on Feb. 7, 2024, 3:02 p.m.