# getFiRiskRegTS: Generic Function for Computation of Finite-Sample Risks In ROptRegTS: Optimally robust estimation for regression-type models

## 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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24``` ```getFiRiskRegTS(risk, ErrorDistr, Regressor, neighbor, ...) ## S4 method for signature ## 'fiUnOvShoot,Norm,UnivariateDistribution,ContNeighborhood' getFiRiskRegTS( risk, ErrorDistr, Regressor, neighbor, clip, stand, sampleSize, Algo, cont) ## S4 method for signature ## 'fiUnOvShoot,Norm,UnivariateDistribution,TotalVarNeighborhood' getFiRiskRegTS( risk, ErrorDistr, Regressor, neighbor, clip, stand, sampleSize, Algo, cont) ## S4 method for signature ## 'fiUnOvShoot,Norm,UnivariateDistribution,CondContNeighborhood' getFiRiskRegTS( risk, ErrorDistr, Regressor, neighbor, clip, stand, sampleSize, cont) ## S4 method for signature ## '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".

## 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).

## 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'.

## Author(s)

Matthias Kohl [email protected]

## 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.

`fiRisk-class`