# getRadius: Computation of the Optimal Radius for Given Clipping Bound In ROptEst: Optimally Robust Estimation

## Description

The usual robust optimality problem for given asGRisk searches the optimal clipping height b of a Hampel-type IC to given radius of the neighborhood. Instead, again for given asGRisk and for given Hampel-Type IC with given clipping height b we may determine the radius of the neighborhood for which it is optimal in the sense of the first sentence.

## Usage

 `1` ```getRadius(IC, risk, neighbor, L2Fam) ```

## Arguments

 `IC` an IC of class `"HampIC"`. `risk` object of class `"RiskType"`. `neighbor` object of class `"Neighborhood"`. `L2Fam` object of class `"L2FamParameter"`. Can be missing; in this case it is constructed from slot `CallL2Fam` of `IC`.

## Author(s)

Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

## References

Rieder, H. (1980) Estimates derived from robust tests. Ann. Stats. 8: 106–115.

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Ruckdeschel, P. and Rieder, H. (2004) Optimal Influence Curves for General Loss Functions. Statistics & Decisions 22, 201-223.

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.

`ContIC-class`, `TotalVarIC-class`
 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```N <- NormLocationFamily(mean=0, sd=1) nb <- ContNeighborhood(); ri <- asMSE() radIC <- radiusMinimaxIC(L2Fam=N, neighbor=nb, risk=ri, loRad=0.1, upRad=0.5) getRadius(radIC, L2Fam=N, neighbor=nb, risk=ri) ## taken from script NormalScaleModel.R in folder scripts N0 <- NormScaleFamily(mean=0, sd=1) (N0.IC7 <- radiusMinimaxIC(L2Fam=N0, neighbor=nb, risk=ri, loRad=0, upRad=Inf)) ## getRadius(N0.IC7, risk=asMSE(), neighbor=nb, L2Fam=N0) getRadius(N0.IC7, risk=asL4(), neighbor=nb, L2Fam=N0) ```