# getAsRisk: Generic Function for Computation of Asymptotic Risks In ROptEstOld: Optimally Robust Estimation - Old Version

## Description

Generic function for the computation of asymptotic risks. This function is rarely called directly. It is used by other functions.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36``` ```getAsRisk(risk, L2deriv, neighbor, ...) ## S4 method for signature 'asMSE,UnivariateDistribution,Neighborhood' getAsRisk(risk, L2deriv, neighbor, clip, cent, stand, trafo) ## S4 method for signature 'asMSE,EuclRandVariable,Neighborhood' getAsRisk(risk, L2deriv, neighbor, clip, cent, stand, trafo) ## S4 method for signature 'asBias,UnivariateDistribution,ContNeighborhood' getAsRisk(risk, L2deriv, neighbor, trafo) ## S4 method for signature 'asBias,UnivariateDistribution,TotalVarNeighborhood' getAsRisk(risk, L2deriv, neighbor, trafo) ## S4 method for signature 'asBias,RealRandVariable,ContNeighborhood' getAsRisk(risk, L2deriv, neighbor, Distr, L2derivDistrSymm, trafo, z.start, A.start, maxiter, tol) ## S4 method for signature 'asCov,UnivariateDistribution,ContNeighborhood' getAsRisk(risk, L2deriv, neighbor, clip, cent, stand) ## S4 method for signature 'asCov,UnivariateDistribution,TotalVarNeighborhood' getAsRisk(risk, L2deriv, neighbor, clip, cent, stand) ## S4 method for signature 'asCov,RealRandVariable,ContNeighborhood' getAsRisk(risk, L2deriv, neighbor, Distr, clip, cent, stand) ## S4 method for signature 'trAsCov,UnivariateDistribution,UncondNeighborhood' getAsRisk(risk, L2deriv, neighbor, clip, cent, stand) ## S4 method for signature 'trAsCov,RealRandVariable,ContNeighborhood' getAsRisk(risk, L2deriv, neighbor, Distr, clip, cent, stand) ## S4 method for signature ## 'asUnOvShoot,UnivariateDistribution,UncondNeighborhood' getAsRisk(risk, L2deriv, neighbor, clip, cent, stand, trafo) ```

## Arguments

 `risk` object of class `"asRisk"`. `L2deriv` L2-derivative of some L2-differentiable family of probability distributions. `neighbor` object of class `"Neighborhood"`. `...` additional parameters. `clip` optimal clipping bound. `cent` optimal centering constant. `stand` standardizing matrix. `trafo` matrix: transformation of the parameter. `Distr` object of class `"Distribution"`. `L2derivDistrSymm` object of class `"DistrSymmList"`. `z.start` initial value for the centering constant. `A.start` initial value for the standardizing matrix. `maxiter` the maximum number of iterations `tol` the desired accuracy (convergence tolerance).

## Value

The asymptotic risk is computed.

## Methods

risk = "asMSE", L2deriv = "UnivariateDistribution", neighbor = "Neighborhood":

computes asymptotic mean square error in methods for function `getInfRobIC`.

risk = "asMSE", L2deriv = "EuclRandVariable", neighbor = "Neighborhood":

computes asymptotic mean square error in methods for function `getInfRobIC`.

risk = "asBias", L2deriv = "UnivariateDistribution", neighbor = "ContNeighborhood":

computes standardized asymptotic bias in methods for function `getInfRobIC`.

risk = "asBias", L2deriv = "UnivariateDistribution", neighbor = "TotalVarNeighborhood":

computes standardized asymptotic bias in methods for function `getInfRobIC`.

risk = "asBias", L2deriv = "RealRandVariable", neighbor = "ContNeighborhood":

computes standardized asymptotic bias in methods for function `getInfRobIC`.

risk = "asCov", L2deriv = "UnivariateDistribution", neighbor = "ContNeighborhood":

computes asymptotic covariance in methods for function `getInfRobIC`.

risk = "asCov", L2deriv = "UnivariateDistribution", neighbor = "TotalVarNeighborhood":

computes asymptotic covariance in methods for function `getInfRobIC`.

risk = "asCov", L2deriv = "RealRandVariable", neighbor = "ContNeighborhood":

computes asymptotic covariance in methods for function `getInfRobIC`.

risk = "trAsCov", L2deriv = "UnivariateDistribution", neighbor = "UncondNeighborhood":

computes trace of asymptotic covariance in methods for function `getInfRobIC`.

risk = "trAsCov", L2deriv = "RealRandVariable", neighbor = "ContNeighborhood":

computes trace of asymptotic covariance in methods for function `getInfRobIC`.

risk = "asUnOvShoot", L2deriv = "UnivariateDistribution", neighbor = "UncondNeighborhood":

computes asymptotic under-/overshoot risk in methods for function `getInfRobIC`.

## Author(s)

Matthias Kohl Matthias.Kohl@stamats.de

## References

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

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

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

`asRisk-class`