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 asMSE,UnivariateDistribution,Neighborhood,ANY
getAsRisk(risk,
    L2deriv, neighbor, biastype, normtype = NULL, clip = NULL, cent = NULL,
    stand, trafo, ...)
# S4 method for asL1,UnivariateDistribution,Neighborhood,ANY
getAsRisk(risk,
    L2deriv, neighbor, biastype, normtype = NULL, clip = NULL, cent = NULL,
    stand, trafo, ...)
# S4 method for asL4,UnivariateDistribution,Neighborhood,ANY
getAsRisk(risk,
    L2deriv, neighbor, biastype, normtype = NULL, clip = NULL, cent = NULL,
    stand, trafo, ...)
# S4 method for asMSE,EuclRandVariable,Neighborhood,ANY
getAsRisk(risk,
    L2deriv, neighbor, biastype, normtype = NULL, clip = NULL, cent = NULL,
    stand, trafo, ...)
# S4 method for asBias,UnivariateDistribution,ContNeighborhood,ANY
getAsRisk(risk,
    L2deriv, neighbor, biastype, normtype = NULL, clip = NULL, cent = NULL,
    stand = NULL, trafo, ...)
# S4 method for asBias,UnivariateDistribution,ContNeighborhood,onesidedBias
getAsRisk(
    risk, L2deriv, neighbor, biastype, normtype = NULL, clip = NULL, cent = NULL,
    stand = NULL, trafo, ...)
# S4 method for asBias,UnivariateDistribution,ContNeighborhood,asymmetricBias
getAsRisk(
    risk, L2deriv, neighbor, biastype, normtype = NULL, clip = NULL, cent = NULL,
    stand = NULL, trafo, ...)
# S4 method for asBias,UnivariateDistribution,TotalVarNeighborhood,ANY
getAsRisk(
    risk, L2deriv, neighbor, biastype, normtype = NULL, clip = NULL, cent = NULL,
    stand = NULL, trafo, ...)
# S4 method for 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 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 asCov,UnivariateDistribution,ContNeighborhood,ANY
getAsRisk(
    risk, L2deriv, neighbor, biastype, normtype = NULL, clip, cent, stand,
    trafo = NULL, ...)
# S4 method for asCov,UnivariateDistribution,TotalVarNeighborhood,ANY
getAsRisk(
    risk, L2deriv, neighbor, biastype, normtype = NULL, clip, cent, stand,
    trafo = NULL, ...)
# S4 method for 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 trAsCov,UnivariateDistribution,UncondNeighborhood,ANY
getAsRisk(
    risk, L2deriv, neighbor, biastype, normtype = NULL, clip, cent, stand,
    trafo = NULL, ...)
# S4 method for 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 asAnscombe,UnivariateDistribution,UncondNeighborhood,ANY
getAsRisk(
    risk, L2deriv, neighbor, biastype, normtype = NULL, clip, cent, stand,
    trafo = NULL, FI, ...)
# S4 method for 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 asUnOvShoot,UnivariateDistribution,UncondNeighborhood,ANY
getAsRisk(
    risk, L2deriv, neighbor, biastype, normtype = NULL, clip, cent, stand,
    trafo, ...)
# S4 method for asSemivar,UnivariateDistribution,Neighborhood,onesidedBias
getAsRisk(
    risk, L2deriv, neighbor, biastype, normtype = NULL, clip, cent, stand,
    trafo, ...)

Value

The asymptotic risk is computed.

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.

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

Matthias Kohl Matthias.Kohl@stamats.de

Details

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

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. tools:::Rd_expr_doi("10.1007/s10260-010-0133-0").

H. Rieder (1994): Robust Asymptotic Statistics. Springer. 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. tools:::Rd_expr_doi("10.1524/stnd.22.3.201.57067")