Generic Function for the Computation of the Optimal Centering Constant/Function resp. Lower Clipping Bound/Function

Description

Generic function for the computation of the optimal centering constant/function (contamination neighborhoods) respectively, of the optimal lower clipping bound/function (total variation neighborhoods). This function is rarely called directly. It is used to compute optimally robust ICs.

Usage

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getInfCentRegTS(ErrorL2deriv, Regressor, neighbor, ...)

## S4 method for signature 
## 'UnivariateDistribution,UnivariateDistribution,ContNeighborhood'
getInfCentRegTS(
             ErrorL2deriv, Regressor, neighbor, clip, cent, stand, z.comp)

## S4 method for signature 
## 'UnivariateDistribution,UnivariateDistribution,TotalVarNeighborhood'
getInfCentRegTS(
             ErrorL2deriv, Regressor, neighbor, clip, cent, z.comp)

## S4 method for signature 
## 'UnivariateDistribution,numeric,CondTotalVarNeighborhood'
getInfCentRegTS(
             ErrorL2deriv, Regressor, neighbor, clip, cent, z.comp)

## S4 method for signature 
## 'UnivariateDistribution,
##   UnivariateDistribution,
##   Av1CondContNeighborhood'
getInfCentRegTS(
             ErrorL2deriv, Regressor, neighbor, clip, cent, stand, z.comp, x.vec)

## S4 method for signature 
## 'UnivariateDistribution,
##   UnivariateDistribution,
##   Av1CondTotalVarNeighborhood'
getInfCentRegTS(
             ErrorL2deriv, Regressor, neighbor, clip, cent, stand, z.comp, x.vec,
             tol.z)

## S4 method for signature 
## 'UnivariateDistribution,MultivariateDistribution,ContNeighborhood'
getInfCentRegTS(
             ErrorL2deriv, Regressor, neighbor, clip, cent, stand, z.comp)

## S4 method for signature 
## 'UnivariateDistribution,
##   MultivariateDistribution,
##   Av1CondContNeighborhood'
getInfCentRegTS(
             ErrorL2deriv, Regressor, neighbor, clip, cent, stand, z.comp, x.vec)

## S4 method for signature 
## 'UnivariateDistribution,Distribution,Av2CondContNeighborhood'
getInfCentRegTS(
             ErrorL2deriv, Regressor, neighbor, clip, cent, stand, z.comp, tol.z)

## S4 method for signature 'RealRandVariable,Distribution,ContNeighborhood'
getInfCentRegTS(
             ErrorL2deriv, Regressor, neighbor, ErrorDistr, stand, cent, clip,
             z.comp)

## S4 method for signature 
## 'RealRandVariable,Distribution,Av1CondContNeighborhood'
getInfCentRegTS(
             ErrorL2deriv, Regressor, neighbor, ErrorDistr, stand, cent, clip,
             z.comp, x.vec)

Arguments

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.

z.comp

which components of the centering constant/function have to be computed.

x.vec

(approximated) support of Regressor.

tol.z

the desired accuracy (convergence tolerance).

ErrorDistr

error distribution.

Value

The optimal centering constant/function is computed.

Methods

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

computation of optimal centering constant.

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

computation of lower clipping bound.

ErrorL2deriv = "UnivariateDistribution", Regressor = "numeric", neighbor = "CondTotalVarNeighborhood"

computation of lower clipping bound.

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

computation of optimal centering function.

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

computation of optimal lower clipping function.

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

computation of optimal centering constant.

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

computation of optimal centering function.

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

computation of optimal lower clipping function.

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

computation of optimal centering constant.

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

computation of optimal centering constant.

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

computation of optimal centering function.

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

ContIC-class, Av1CondContIC-class, Av2CondContIC-class, Av1CondTotalVarIC-class, CondContIC-class, CondTotalVarIC-class

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