# leastFavorableRadius: Generic Function for the Computation of Least Favorable Radii In ROptEst: Optimally Robust Estimation

## Description

Generic function for the computation of least favorable radii.

## Usage

 ```1 2 3 4 5 6 7 8``` ```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 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 `...` 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 [email protected]ats.de, Peter Ruckdeschel [email protected]

## 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.

`radiusMinimaxIC`
 ```1 2 3``` ```N <- NormLocationFamily(mean=0, sd=1) leastFavorableRadius(L2Fam=N, neighbor=ContNeighborhood(), risk=asMSE(), rho=0.5) ```