Generic Function for Computation of Asymptotic Risks in case of RegressionType Models
Description
Generic function for the computation of asymptotic risks in case of regressiontype models. This function is rarely called directly. It is used by other functions.
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 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103  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 
ErrorL2deriv 
L2derivative of 
Regressor 
regressor. 
neighbor 
object of class 
... 
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 
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
asRiskclass