getFiRiskRegTS: Generic Function for Computation of Finite-Sample Risks

Description

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

Usage

getFiRiskRegTS(risk, ErrorDistr, Regressor, neighbor, ...)
# S4 method for fiUnOvShoot,Norm,UnivariateDistribution,ContNeighborhood
getFiRiskRegTS(
             risk, ErrorDistr, Regressor, neighbor, clip, stand, sampleSize,
             Algo, cont)
# S4 method for fiUnOvShoot,Norm,UnivariateDistribution,TotalVarNeighborhood
getFiRiskRegTS(
             risk, ErrorDistr, Regressor, neighbor, clip, stand, sampleSize,
             Algo, cont)
# S4 method for fiUnOvShoot,Norm,UnivariateDistribution,CondContNeighborhood
getFiRiskRegTS(
             risk, ErrorDistr, Regressor, neighbor, clip, stand, sampleSize,
             cont)
# S4 method for fiUnOvShoot,Norm,UnivariateDistribution,CondTotalVarNeighborhood
getFiRiskRegTS(
             risk, ErrorDistr, Regressor, neighbor, clip, stand, sampleSize, cont)

Arguments

risk

object of class "RiskType".

ErrorDistr

error distribution

Regressor

regressor

neighbor

object of class "Neighborhood".

…

additional parameters.

clip

optimal clipping bound/function.

stand

standardizing matrix.

sampleSize

integer: sample size.

Algo

"A" or "B".

cont

"left" or "right".

Value

The finite-sample risk is computed.

Methods

risk = "fiUnOvShoot", ErrorDistr = "Norm", Regressor = "UnivariateDistribution", neighbor = "ContNeighborhood": computes finite-sample under-/overshoot risk in methods for function 'getFixRobRegTypeIC'.
risk = "fiUnOvShoot", ErrorDistr = "Norm", Regressor = "UnivariateDistribution", neighbor = "TotalVarNeighborhood": computes finite-sample under-/overshoot risk in methods for function 'getFixRobRegTypeIC'.
risk = "fiUnOvShoot", ErrorDistr = "Norm", Regressor = "UnivariateDistribution", neighbor = "CondContNeighborhood": computes finite-sample under-/overshoot risk in methods for function 'getFixRobRegTypeIC'.
risk = "fiUnOvShoot", ErrorDistr = "Norm", Regressor = "UnivariateDistribution", neighbor = "CondTotalVarNeighborhood": computes finite-sample under-/overshoot risk in methods for function 'getFixRobRegTypeIC'.

Details

The computation of the finite-sample under-/overshoot risk is based on FFT. For more details we refer to Subsections 12.1.3 and 12.2.3 of Kohl (2005).

References

Huber, P.J. (1968) Robust Confidence Limits. Z. Wahrscheinlichkeitstheor. Verw. Geb. 10:269--278.

Rieder, H. (1989) A finite-sample minimax regression estimator. Statistics 20(2): 211--221.

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