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
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59  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 
L2derivative of 
Regressor 
regressor. 
neighbor 
object of class 
... 
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 
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
ContICclass
, Av1CondContICclass
,
Av2CondContICclass
, Av1CondTotalVarICclass
,
CondContICclass
, CondTotalVarICclass