Generic Function for the Computation of Optimally Robust Regression-Type ICs

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Description

Generic function for the computation of optimally robust regression-type ICs in case of infinitesimal robust models. This function is rarely called directly.

Usage

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

## S4 method for signature 
## 'UnivariateDistribution,
##   UnivariateDistribution,
##   asBias,
##   ContNeighborhood'
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorL2derivDistrSymm,
             RegSymm, Finfo, trafo, upper, maxiter, tol, warn)

## S4 method for signature 
## 'UnivariateDistribution,
##   UnivariateDistribution,
##   asBias,
##   Av1CondContNeighborhood'
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorL2derivDistrSymm,
             RegSymm, Finfo, trafo, upper, maxiter, tol, warn)

## S4 method for signature 
## 'UnivariateDistribution,
##   UnivariateDistribution,
##   asBias,
##   Av1CondTotalVarNeighborhood'
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorL2derivDistrSymm,
             RegSymm, Finfo, trafo, upper, maxiter, tol, warn)

## S4 method for signature 
## 'UnivariateDistribution,Distribution,asBias,Av2CondContNeighborhood'
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorL2derivDistrSymm,
             RegSymm, Finfo, trafo, upper, maxiter, tol, warn)

## S4 method for signature 
## 'UnivariateDistribution,Distribution,asCov,ContNeighborhood'
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorL2derivDistrSymm,
             RegSymm, Finfo, trafo)

## S4 method for signature 
## 'UnivariateDistribution,
##   UnivariateDistribution,
##   asCov,
##   TotalVarNeighborhood'
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorL2derivDistrSymm,
             RegSymm, Finfo, trafo)

## S4 method for signature 
## 'UnivariateDistribution,Distribution,asCov,CondContNeighborhood'
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorL2derivDistrSymm,
             RegSymm, Finfo, trafo)

## S4 method for signature 
## 'UnivariateDistribution,Distribution,asCov,CondTotalVarNeighborhood'
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorL2derivDistrSymm,
             RegSymm, Finfo, trafo)

## S4 method for signature 
## 'UnivariateDistribution,Distribution,asCov,Av1CondContNeighborhood'
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorL2derivDistrSymm,
             RegSymm, Finfo, trafo)

## S4 method for signature 
## 'UnivariateDistribution,Distribution,asCov,Av2CondContNeighborhood'
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorL2derivDistrSymm,
             RegSymm, Finfo, trafo)

## S4 method for signature 
## 'UnivariateDistribution,
##   Distribution,
##   asCov,
##   Av1CondTotalVarNeighborhood'
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorL2derivDistrSymm,
             RegSymm, Finfo, trafo)

## S4 method for signature 
## 'UnivariateDistribution,Distribution,asGRisk,ContNeighborhood'
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorL2derivDistrSymm,
             RegSymm, Finfo, trafo, upper, maxiter, tol, warn)

## S4 method for signature 
## 'UnivariateDistribution,Distribution,asGRisk,Av1CondContNeighborhood'
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorL2derivDistrSymm,
             RegSymm, Finfo, trafo, upper, maxiter, tol, warn)

## S4 method for signature 
## 'UnivariateDistribution,Distribution,asGRisk,Av2CondContNeighborhood'
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorL2derivDistrSymm,
             RegSymm, Finfo, trafo, upper, maxiter, tol, warn)

## S4 method for signature 
## 'UnivariateDistribution,
##   Distribution,
##   asGRisk,
##   Av1CondTotalVarNeighborhood'
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorL2derivDistrSymm,
             RegSymm, Finfo, trafo, upper, maxiter, tol, warn)

## S4 method for signature 
## 'UnivariateDistribution,
##   MultivariateDistribution,
##   asBias,
##   ContNeighborhood'
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorL2derivDistrSymm,
             RegSymm, Finfo, trafo, upper, maxiter, tol, warn)

## S4 method for signature 
## 'UnivariateDistribution,
##   MultivariateDistribution,
##   asBias,
##   Av1CondContNeighborhood'
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorL2derivDistrSymm,
             RegSymm, Finfo, trafo, upper, maxiter, tol, warn)

## S4 method for signature 
## 'UnivariateDistribution,
##   MultivariateDistribution,
##   asBias,
##   Av1CondTotalVarNeighborhood'
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorL2derivDistrSymm,
             RegSymm, Finfo, trafo, upper, maxiter, tol, warn)

## S4 method for signature 
## 'RealRandVariable,Distribution,asBias,ContNeighborhood'
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorSymm, RegSymm,
             ErrorDistr, ErrorL2derivSymm, ErrorL2derivDistrSymm, Finfo, trafo,
             upper, z.start, A.start, maxiter, tol, warn)

## S4 method for signature 
## 'RealRandVariable,Distribution,asBias,Av1CondContNeighborhood'
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorSymm, RegSymm,
             ErrorDistr, ErrorL2derivSymm, ErrorL2derivDistrSymm, Finfo, trafo,
             upper, z.start, A.start, maxiter, tol, warn)

## S4 method for signature 
## 'RealRandVariable,Distribution,asCov,ContNeighborhood'
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorDistr, Finfo, trafo)

## S4 method for signature 
## 'RealRandVariable,Distribution,asCov,Av1CondContNeighborhood'
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorDistr, Finfo, trafo)

## S4 method for signature 
## 'RealRandVariable,Distribution,asGRisk,ContNeighborhood'
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorSymm, RegSymm,
             ErrorDistr, ErrorL2derivSymm, ErrorL2derivDistrSymm, Finfo, trafo,
             upper, z.start, A.start, maxiter, tol, warn)

## S4 method for signature 
## 'RealRandVariable,Distribution,asGRisk,Av1CondContNeighborhood'
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorSymm, RegSymm,
             ErrorDistr, ErrorL2derivSymm, ErrorL2derivDistrSymm, Finfo, trafo,
             upper, z.start, A.start, maxiter, tol, warn)

## S4 method for signature 
## 'UnivariateDistribution,
##   UnivariateDistribution,
##   asUnOvShoot,
##   UncondNeighborhood'
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorL2derivDistrSymm,
             RegSymm, Finfo, trafo, upper, maxiter, tol, warn)

## S4 method for signature 
## 'UnivariateDistribution,
##   UnivariateDistribution,
##   asUnOvShoot,
##   CondNeighborhood'
getInfRobRegTypeIC(
             ErrorL2deriv, Regressor, risk, neighbor, ErrorL2derivDistrSymm,
             RegSymm, Finfo, trafo, upper, maxiter, tol, warn)

Arguments

ErrorL2deriv

L2-derivative of ErrorDistr.

Regressor

regressor.

risk

object of class "RiskType".

neighbor

object of class "Neighborhood".

...

additional parameters.

ErrorSymm

symmetry of ErrorDistr.

ErrorL2derivDistrSymm

symmetry of ErrorL2derivDistr.

RegSymm

symmetry of RegDistr.

ErrorDistr

error distribution.

ErrorL2derivSymm

symmetry of ErrorL2deriv.

Finfo

Fisher information matrix.

trafo

matrix: transformation of the parameter.

upper

upper bound for the optimal clipping bound.

maxiter

the maximum number of iterations

tol

the desired accuracy (convergence tolerance).

warn

logical: print warnings.

z.start

initial value for the centering constant/function.

A.start

initial value for the standardizing matrix.

Value

The optimally robust IC is computed.

Methods

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

computes the bias optimal influence curve for L2 differentiable regression-type families.

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

computes the bias optimal influence curve for L2 differentiable regression-type families.

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

computes the bias optimal influence curve for L2 differentiable regression-type families.

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

computes the bias optimal influence curve for L2 differentiable regression-type families.

ErrorL2deriv = "UnivariateDistribution", Regressor = "Distribution", risk = "asCov", neighbor = "ContNeighborhood"

computes the classical optimal influence curve for L2 differentiable regression-type families.

ErrorL2deriv = "UnivariateDistribution", Regressor = "UnivariateDistribution", risk = "asCov", neighbor = "TotalVarNeighborhood"

computes the classical optimal influence curve for L2 differentiable regression-type families.

ErrorL2deriv = "UnivariateDistribution", Regressor = "Distribution", risk = "asCov", neighbor = "CondContNeighborhood"

computes the classical optimal influence curve for L2 differentiable regression-type families.

ErrorL2deriv = "UnivariateDistribution", Regressor = "Distribution", risk = "asCov", neighbor = "CondTotalVarNeighborhood"

computes the classical optimal influence curve for L2 differentiable regression-type families.

ErrorL2deriv = "UnivariateDistribution", Regressor = "Distribution", risk = "asCov", neighbor = "Av1CondContNeighborhood"

computes the classical optimal influence curve for L2 differentiable regression-type families.

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

computes the classical optimal influence curve for L2 differentiable regression-type families.

ErrorL2deriv = "UnivariateDistribution", Regressor = "Distribution", risk = "asCov", neighbor = "Av1CondTotalVarNeighborhood"

computes the classical optimal influence curve for L2 differentiable regression-type families.

ErrorL2deriv = "UnivariateDistribution", Regressor = "Distribution", risk = "asGRisk", neighbor = "ContNeighborhood"

computes the optimally robust influence curve for L2 differentiable regression-type families.

ErrorL2deriv = "UnivariateDistribution", Regressor = "Distribution", risk = "asGRisk", neighbor = "Av1CondContNeighborhood"

computes the optimally robust influence curve for L2 differentiable regression-type families.

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

computes the optimally robust influence curve for L2 differentiable regression-type families.

ErrorL2deriv = "UnivariateDistribution", Regressor = "Distribution", risk = "asGRisk", neighbor = "Av1CondTotalVarNeighborhood"

computes the optimally robust influence curve for L2 differentiable regression-type families.

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

computes the bias optimal influence curve for L2 differentiable regression-type families.

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

computes the bias optimal influence curve for L2 differentiable regression-type families.

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

computes the bias optimal influence curve for L2 differentiable regression-type families.

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

computes the bias optimal influence curve for L2 differentiable regression-type families.

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

computes the classical optimal influence curve for L2 differentiable regression-type families.

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

computes the classical optimal influence curve for L2 differentiable regression-type families.

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

computes the optimally robust influence curve for L2 differentiable regression-type families.

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

computes the optimally robust influence curve for L2 differentiable regression-type families.

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

computes the optimally robust influence curve for L2 differentiable regression-type families.

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

computes the optimally robust influence curve for L2 differentiable regression-type families.

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.

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

See Also

InfRobRegTypeModel-class

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