getAsRisk {ROptEst}R Documentation

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

M. Kohl (2005). Numerical Contributions to the Asymptotic Theory of Robustness. Dissertation. University of Bayreuth. https://epub.uni-bayreuth.de/id/eprint/839/2/DissMKohl.pdf.

M. Kohl, P. Ruckdeschel, and H. Rieder (2010). Infinitesimally Robust Estimation in General Smoothly Parametrized Models. Statistical Methods and Applications 19(3): 333-354. doi:10.1007/s10260-010-0133-0.

H. Rieder (1994): Robust Asymptotic Statistics. Springer. doi:10.1007/978-1-4684-0624-5

P. Ruckdeschel (2005). Optimally One-Sided Bounded Influence Curves. Mathematical Methods of Statistics 14(1), 105-131.

P. Ruckdeschel and H. Rieder (2004). Optimal Influence Curves for General Loss Functions. Statistics & Decisions 22, 201-223. doi:10.1524/stnd.22.3.201.57067

See Also

asRisk-class

[Package ROptEst version 1.3.3 Index]