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getAsRiskRegTS: Generic Function for Computation of Asymptotic Risks in case...

Description Usage Arguments Value Methods Author(s) References See Also

Description

Generic function for the computation of asymptotic risks in case of regression-type models. This function is rarely called directly. It is used by other functions.

Usage

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getAsRiskRegTS(risk, ErrorL2deriv, Regressor, neighbor, ...)

## S4 method for signature 
## 'asMSE,UnivariateDistribution,Distribution,Neighborhood'
getAsRiskRegTS(
             risk, ErrorL2deriv, Regressor, neighbor, clip, cent, stand, trafo)

## S4 method for signature 
## 'asMSE,UnivariateDistribution,Distribution,Av2CondContNeighborhood'
getAsRiskRegTS(
             risk, ErrorL2deriv, Regressor, neighbor, clip, cent, stand, trafo)

## S4 method for signature 'asMSE,EuclRandVariable,Distribution,Neighborhood'
getAsRiskRegTS(
             risk, ErrorL2deriv, Regressor, neighbor, clip, cent, stand, trafo)

## S4 method for signature 
## 'asBias,
##   UnivariateDistribution,
##   UnivariateDistribution,
##   ContNeighborhood'
getAsRiskRegTS(
             risk, ErrorL2deriv, Regressor, neighbor, ErrorL2derivDistrSymm,
             trafo, maxiter, tol)

## S4 method for signature 
## 'asBias,
##   UnivariateDistribution,
##   UnivariateDistribution,
##   Av1CondContNeighborhood'
getAsRiskRegTS(
             risk, ErrorL2deriv, Regressor, neighbor, ErrorL2derivDistrSymm,
             trafo, maxiter, tol)

## S4 method for signature 
## 'asBias,
##   UnivariateDistribution,
##   UnivariateDistribution,
##   Av1CondTotalVarNeighborhood'
getAsRiskRegTS(
             risk, ErrorL2deriv, Regressor, neighbor, ErrorL2derivDistrSymm,
             trafo, maxiter, tol)

## S4 method for signature 
## 'asBias,
##   UnivariateDistribution,
##   MultivariateDistribution,
##   ContNeighborhood'
getAsRiskRegTS(
             risk, ErrorL2deriv, Regressor, neighbor, ErrorL2derivDistrSymm,
             trafo, maxiter, tol)

## S4 method for signature 
## 'asBias,
##   UnivariateDistribution,
##   MultivariateDistribution,
##   Av1CondContNeighborhood'
getAsRiskRegTS(
             risk, ErrorL2deriv, Regressor, neighbor, ErrorL2derivDistrSymm,
             trafo, maxiter, tol)

## S4 method for signature 
## 'asBias,
##   UnivariateDistribution,
##   MultivariateDistribution,
##   Av1CondTotalVarNeighborhood'
getAsRiskRegTS(
             risk, ErrorL2deriv, Regressor, neighbor, ErrorL2derivDistrSymm,
             trafo, maxiter, tol)

## S4 method for signature 
## 'asBias,UnivariateDistribution,Distribution,Av2CondContNeighborhood'
getAsRiskRegTS(
             risk, ErrorL2deriv, Regressor, neighbor, ErrorL2derivDistrSymm,
             trafo, maxiter, tol)

## S4 method for signature 
## 'asBias,RealRandVariable,Distribution,ContNeighborhood'
getAsRiskRegTS(
             risk, ErrorL2deriv, Regressor, neighbor, ErrorDistr, trafo, z.start,
             A.start, maxiter, tol)

## S4 method for signature 
## 'asBias,RealRandVariable,Distribution,Av1CondContNeighborhood'
getAsRiskRegTS(
             risk, ErrorL2deriv, Regressor, neighbor, ErrorDistr, trafo, z.start,
             A.start, maxiter, tol)

## S4 method for signature 
## 'asUnOvShoot,
##   UnivariateDistribution,
##   UnivariateDistribution,
##   UncondNeighborhood'
getAsRiskRegTS(
             risk, ErrorL2deriv, Regressor, neighbor, clip, cent, stand)

## S4 method for signature 
## 'asUnOvShoot,
##   UnivariateDistribution,
##   UnivariateDistribution,
##   CondNeighborhood'
getAsRiskRegTS(
             risk, ErrorL2deriv, Regressor, neighbor, clip, cent, stand)

Arguments

risk

object of class "asRisk".

ErrorL2deriv

L2-derivative of ErrorDistr.

Regressor

regressor.

neighbor

object of class "Neighborhood".

...

additional parameters.

clip

optimal clipping bound.

cent

optimal centering constant/function.

stand

standardizing matrix.

trafo

matrix: transformation of the parameter.

ErrorDistr

error distribution.

ErrorL2derivDistrSymm

symmetry of ErrorL2derivDistr.

maxiter

the maximum number of iterations

tol

the desired accuracy (convergence tolerance).

z.start

initial value for the centering constant/function.

A.start

initial value for the standardizing matrix.

Value

The asymptotic risk is computed.

Methods

risk = "asMSE", ErrorL2deriv = "UnivariateDistribution", Regressor = "Distribution", neighbor = "Neighborhood"

computes asymptotic mean square error in methods for function getInfRobRegTypeIC.

risk = "asMSE", ErrorL2deriv = "UnivariateDistribution", Regressor = "Distribution", neighbor = "Av2CondContNeighborhood"

computes asymptotic mean square error in methods for function getInfRobRegTypeIC.

risk = "asMSE", ErrorL2deriv = "EuclRandVariable", Regressor = "Distribution", neighbor = "Neighborhood"

computes asymptotic mean square error in methods for function getInfRobRegTypeIC.

risk = "asBias", ErrorL2deriv = "UnivariateDistribution", Regressor = "UnivariateDistribution", neighbor = "ContNeighborhood"

computes standardized asymptotic bias in methods for function getInfRobRegTypeIC.

risk = "asBias", ErrorL2deriv = "UnivariateDistribution", Regressor = "UnivariateDistribution", neighbor = "Av1CondContNeighborhood"

computes standardized asymptotic bias in methods for function getInfRobRegTypeIC.

risk = "asBias", ErrorL2deriv = "UnivariateDistribution", Regressor = "UnivariateDistribution", neighbor = "Av1CondTotalVarNeighborhood"

computes standardized asymptotic bias in methods for function getInfRobRegTypeIC.

risk = "asBias", ErrorL2deriv = "UnivariateDistribution", Regressor = "MultivariateDistribution", neighbor = "ContNeighborhood"

computes standardized asymptotic bias in methods for function getInfRobRegTypeIC.

risk = "asBias", ErrorL2deriv = "UnivariateDistribution", Regressor = "MultivariateDistribution", neighbor = "Av1CondContNeighborhood"

computes standardized asymptotic bias in methods for function getInfRobRegTypeIC.

risk = "asBias", ErrorL2deriv = "UnivariateDistribution", Regressor = "MultivariateDistribution", neighbor = "Av1CondTotalVarNeighborhood"

computes standardized asymptotic bias in methods for function getInfRobRegTypeIC.

risk = "asBias", ErrorL2deriv = "UnivariateDistribution", Regressor = "Distribution", neighbor = "Av2CondContNeighborhood"

computes standardized asymptotic bias in methods for function getInfRobRegTypeIC.

risk = "asBias", ErrorL2deriv = "RealRandVariable", Regressor = "Distribution", neighbor = "ContNeighborhood"

computes standardized asymptotic bias in methods for function getInfRobRegTypeIC.

risk = "asBias", ErrorL2deriv = "RealRandVariable", Regressor = "Distribution", neighbor = "Av1CondContNeighborhood"

computes standardized asymptotic bias in methods for function getInfRobRegTypeIC.

risk = "asUnOvShoot", ErrorL2deriv = "UnivariateDistribution", Regressor = "UnivariateDistribution", neighbor = "UncondNeighborhood"

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

risk = "asUnOvShoot", ErrorL2deriv = "UnivariateDistribution", Regressor = "UnivariateDistribution", neighbor = "CondNeighborhood"

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

Author(s)

Matthias Kohl Matthias.Kohl@stamats.de

References

Rieder, H. (1980) Estimates derived from robust tests. Ann. Stats. 8: 106–115.

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Ruckdeschel, P. and Rieder, H. (2004) Optimal Influence Curves for General Loss Functions. Statistics & Decisions (submitted).

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

asRisk-class



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