# optRisk: Generic function for the computation of the minimal risk In ROptEst: Optimally Robust Estimation

## Description

Generic function for the computation of the optimal (i.e., minimal) risk for a probability model.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ```optRisk(model, risk, ...) ## S4 method for signature 'L2ParamFamily,asCov' optRisk(model, risk) ## S4 method for signature 'InfRobModel,asRisk' optRisk(model, risk, z.start = NULL, A.start = NULL, upper = 1e4, maxiter = 50, tol = .Machine\$double.eps^0.4, warn = TRUE, noLow = FALSE) ## S4 method for signature 'FixRobModel,fiUnOvShoot' optRisk(model, risk, sampleSize, upper = 1e4, maxiter = 50, tol = .Machine\$double.eps^0.4, warn = TRUE, Algo = "A", cont = "left") ```

## Arguments

 `model` probability model `risk` object of class `RiskType` `...` additional parameters `z.start` initial value for the centering constant. `A.start` initial value for the standardizing matrix. `upper` upper bound for the optimal clipping bound. `maxiter` the maximum number of iterations `tol` the desired accuracy (convergence tolerance). `warn` logical: print warnings. `sampleSize` integer: sample size. `Algo` "A" or "B". `cont` "left" or "right". `noLow` logical: is lower case to be computed?

## Details

In case of the finite-sample risk `"fiUnOvShoot"` one can choose between two algorithms for the computation of this risk where the least favorable contamination is assumed to be left or right of some bound. For more details we refer to Section 11.3 of Kohl (2005).

## Value

The minimal risk is computed.

## Methods

model = "L2ParamFamily", risk = "asCov"

asymptotic covariance of L2 differentiable parameteric family.

model = "InfRobModel", risk = "asRisk"

asymptotic risk of a infinitesimal robust model.

model = "FixRobModel", risk = "fiUnOvShoot"

finite-sample under-/overshoot risk of a robust model with fixed neighborhood.

## Author(s)

Matthias Kohl Matthias.Kohl@stamats.de

## References

Huber, P.J. (1968) Robust Confidence Limits. Z. Wahrscheinlichkeitstheor. Verw. Geb. 10:269–278.

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

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

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

`RiskType-class`
 `1` ```optRisk(model = NormLocationScaleFamily(), risk = asCov()) ```