ROptEst: getAsRisk – R documentation

Become an expert in R — Interactive courses, Cheat Sheets, certificates and more!

getAsRisk

Generic Function for Computation of Asymptotic Risks

Description

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

Usage

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.