ROptEst (version 1.0)

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, ...)
"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".

...

additional parameters

upRad

the upper end point of the radius interval to be searched.

rho

The considered radius interval is: $[r*rho, r/rho]$ with $0 < rho < 1$.

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

Value

The least favorable radius and the corresponding inefficiency are computed.

Methods

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. Submitted. 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

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

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

radiusMinimaxIC

Examples

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