# getAsRisk: Generic Function for Computation of Asymptotic Risks In ROptEst: Optimally Robust Estimation

## 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 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111``` ```getAsRisk(risk, L2deriv, neighbor, biastype, ...) ## S4 method for signature 'asMSE,UnivariateDistribution,Neighborhood,ANY' getAsRisk(risk, L2deriv, neighbor, biastype, normtype = NULL, clip = NULL, cent = NULL, stand, trafo, ...) ## S4 method for signature 'asL1,UnivariateDistribution,Neighborhood,ANY' getAsRisk(risk, L2deriv, neighbor, biastype, normtype = NULL, clip = NULL, cent = NULL, stand, trafo, ...) ## S4 method for signature 'asL4,UnivariateDistribution,Neighborhood,ANY' getAsRisk(risk, L2deriv, neighbor, biastype, normtype = NULL, clip = NULL, cent = NULL, stand, trafo, ...) ## S4 method for signature 'asMSE,EuclRandVariable,Neighborhood,ANY' getAsRisk(risk, L2deriv, neighbor, biastype, normtype = NULL, clip = NULL, cent = NULL, stand, trafo, ...) ## S4 method for signature 'asBias,UnivariateDistribution,ContNeighborhood,ANY' getAsRisk(risk, L2deriv, neighbor, biastype, normtype = NULL, clip = NULL, cent = NULL, stand = NULL, trafo, ...) ## S4 method for signature ## 'asBias,UnivariateDistribution,ContNeighborhood,onesidedBias' getAsRisk( risk, L2deriv, neighbor, biastype, normtype = NULL, clip = NULL, cent = NULL, stand = NULL, trafo, ...) ## S4 method for signature ## 'asBias,UnivariateDistribution,ContNeighborhood,asymmetricBias' getAsRisk( risk, L2deriv, neighbor, biastype, normtype = NULL, clip = NULL, cent = NULL, stand = NULL, trafo, ...) ## S4 method for signature ## 'asBias,UnivariateDistribution,TotalVarNeighborhood,ANY' getAsRisk( risk, L2deriv, neighbor, biastype, normtype = NULL, clip = NULL, cent = NULL, stand = NULL, trafo, ...) ## S4 method for signature 'asBias,RealRandVariable,ContNeighborhood,ANY' getAsRisk( risk,L2deriv, neighbor, biastype, normtype = NULL, clip = NULL, cent = NULL, stand = NULL, Distr, DistrSymm, L2derivSymm, L2derivDistrSymm, Finfo, trafo, z.start, A.start, maxiter, tol, warn, verbose = NULL, ...) ## S4 method for signature 'asBias,RealRandVariable,TotalVarNeighborhood,ANY' getAsRisk( risk, L2deriv, neighbor, biastype, normtype = NULL, clip = NULL, cent = NULL, stand = NULL, Distr, DistrSymm, L2derivSymm, L2derivDistrSymm, Finfo, trafo, z.start, A.start, maxiter, tol, warn, verbose = NULL, ...) ## S4 method for signature 'asCov,UnivariateDistribution,ContNeighborhood,ANY' getAsRisk( risk, L2deriv, neighbor, biastype, normtype = NULL, clip, cent, stand, trafo = NULL, ...) ## S4 method for signature ## 'asCov,UnivariateDistribution,TotalVarNeighborhood,ANY' getAsRisk( risk, L2deriv, neighbor, biastype, normtype = NULL, clip, cent, stand, trafo = NULL, ...) ## S4 method for signature 'asCov,RealRandVariable,ContNeighborhood,ANY' getAsRisk(risk, L2deriv, neighbor, biastype, normtype = NULL, clip = NULL, cent, stand, Distr, trafo = NULL, V.comp = matrix(TRUE, ncol = nrow(stand), nrow = nrow(stand)), w, ...) ## S4 method for signature ## 'trAsCov,UnivariateDistribution,UncondNeighborhood,ANY' getAsRisk( risk, L2deriv, neighbor, biastype, normtype = NULL, clip, cent, stand, trafo = NULL, ...) ## S4 method for signature 'trAsCov,RealRandVariable,ContNeighborhood,ANY' getAsRisk(risk, L2deriv, neighbor, biastype, normtype, clip, cent, stand, Distr, trafo = NULL, V.comp = matrix(TRUE, ncol = nrow(stand), nrow = nrow(stand)), w, ...) ## S4 method for signature ## 'asAnscombe,UnivariateDistribution,UncondNeighborhood,ANY' getAsRisk( risk, L2deriv, neighbor, biastype, normtype = NULL, clip, cent, stand, trafo = NULL, FI, ...) ## S4 method for signature 'asAnscombe,RealRandVariable,ContNeighborhood,ANY' getAsRisk(risk, L2deriv, neighbor, biastype, normtype, clip, cent, stand, Distr, trafo = NULL, V.comp = matrix(TRUE, ncol = nrow(stand), nrow = nrow(stand)), FI, w, ...) ## S4 method for signature ## 'asUnOvShoot,UnivariateDistribution,UncondNeighborhood,ANY' getAsRisk( risk, L2deriv, neighbor, biastype, normtype = NULL, clip, cent, stand, trafo, ...) ## S4 method for signature ## 'asSemivar,UnivariateDistribution,Neighborhood,onesidedBias' getAsRisk( risk, L2deriv, neighbor, biastype, normtype = NULL, 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"`. `biastype` object of class `"ANY"`. `...` additional parameters; often used to enable flexible calls. `clip` optimal clipping bound. `cent` optimal centering constant. `stand` standardizing matrix. `Finfo` matrix: the Fisher Information of the parameter. `trafo` matrix: transformation of the parameter. `Distr` object of class `"Distribution"`. `DistrSymm` object of class `"DistributionSymmetry"`. `L2derivSymm` object of class `"FunSymmList"`. `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). `warn` logical: print warnings. `normtype` object of class `"NormType"`. `V.comp` matrix: indication which components of the standardizing matrix have to be computed. `w` object of class `RobWeight`; current weight `FI` trace of the respective Fisher Information `verbose` logical: if `TRUE` some diagnostics are printed out.

## Details

This function is rarely called directly. It is used by other functions/methods.

## Value

The asymptotic risk is computed.

## Methods

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

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

risk = "asL1", L2deriv = "UnivariateDistribution", neighbor = "Neighborhood", biastype = "ANY":

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

risk = "asL4", L2deriv = "UnivariateDistribution", neighbor = "Neighborhood", biastype = "ANY":

computes asymptotic mean power 4 error in methods for function `getInfRobIC`.

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

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

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

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

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

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

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

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

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

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

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

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

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

computes asymptotic covariance in methods for function `getInfRobIC`.

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

computes asymptotic covariance in methods for function `getInfRobIC`.

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

computes asymptotic covariance in methods for function `getInfRobIC`.

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

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

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

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

risk = "asAnscombe", L2deriv = "UnivariateDistribution", neighbor = "UncondNeighborhood", biastype = "ANY":

computes the ARE in the ideal model in methods for function `getInfRobIC`.

risk = "asAnscombe", L2deriv = "RealRandVariable", neighbor = "ContNeighborhood", biastype = "ANY":

computes the ARE in the ideal model in methods for function `getInfRobIC`.

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

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

risk = "asSemivar", L2deriv = "UnivariateDistribution", neighbor = "Neighborhood", biastype = "onesidedBias":

computes asymptotic semivariance 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 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.

`asRisk-class`