getAsRisk: Generic Function for Computation of Asymptotic Risks

In ROptEst: Optimally Robust Estimation

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 [e-mail]

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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s10260-010-0133-0")}.

H. Rieder (1994): Robust Asymptotic Statistics. Springer. \Sexpr[results=rd]{tools:::Rd_expr_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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1524/stnd.22.3.201.57067")}

See Also

asRisk-class

ROptEst documentation built on Jan. 12, 2025, 3:01 a.m.