# getInfRad: Generic Function for the Computation of the Optimal Radius... In ROptEst: Optimally Robust Estimation

## Description

The usual robust optimality problem for given asGRisk searches the optimal clipping height b of a Hampel-type IC to given radius of the neighborhood. Instead, again for given asGRisk and for given Hampel-Type IC with given clipping height b we may determine the radius of the neighborhood for which it is optimal in the sense of the first sentence. This radius is determined by `getInfRad`. This function is rarely called directly. It is used withing `getRadius`.

## 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``` ```getInfRad(clip, L2deriv, risk, neighbor, ...) ## S4 method for signature ## 'numeric,UnivariateDistribution,asMSE,ContNeighborhood' getInfRad( clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo) ## S4 method for signature ## 'numeric,UnivariateDistribution,asMSE,TotalVarNeighborhood' getInfRad( clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo) ## S4 method for signature ## 'numeric,UnivariateDistribution,asL1,ContNeighborhood' getInfRad( clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo) ## S4 method for signature ## 'numeric,UnivariateDistribution,asL1,TotalVarNeighborhood' getInfRad( clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo) ## S4 method for signature ## 'numeric,UnivariateDistribution,asL4,ContNeighborhood' getInfRad( clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo) ## S4 method for signature ## 'numeric,UnivariateDistribution,asL4,TotalVarNeighborhood' getInfRad( clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo) ## S4 method for signature 'numeric,EuclRandVariable,asMSE,UncondNeighborhood' getInfRad( clip, L2deriv, risk, neighbor, biastype, Distr, stand, cent, trafo, ...) ## S4 method for signature ## 'numeric,UnivariateDistribution,asUnOvShoot,UncondNeighborhood' getInfRad( clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo) ## S4 method for signature ## 'numeric,UnivariateDistribution,asSemivar,ContNeighborhood' getInfRad( clip, L2deriv, risk, neighbor, biastype, cent, symm, trafo) ```

## Arguments

 `clip` positive real: clipping bound `L2deriv` L2-derivative of some L2-differentiable family of probability measures. `risk` object of class `"RiskType"`. `neighbor` object of class `"Neighborhood"`. `...` additional parameters. `biastype` object of class `"BiasType"` `cent` optimal centering constant. `stand` standardizing matrix. `Distr` object of class `"Distribution"`. `symm` logical: indicating symmetry of `L2deriv`. `trafo` matrix: transformation of the parameter.

## Value

The optimal clipping bound is computed.

## Methods

clip = "numeric", L2deriv = "UnivariateDistribution", risk = "asMSE", neighbor = "ContNeighborhood"

optimal clipping bound for asymtotic mean square error.

clip = "numeric", L2deriv = "UnivariateDistribution", risk = "asMSE", neighbor = "TotalVarNeighborhood"

optimal clipping bound for asymtotic mean square error.

clip = "numeric", L2deriv = "EuclRandVariable", risk = "asMSE", neighbor = "UncondNeighborhood"

optimal clipping bound for asymtotic mean square error.

clip = "numeric", L2deriv = "UnivariateDistribution", risk = "asL1", neighbor = "ContNeighborhood"

optimal clipping bound for asymtotic mean absolute error.

clip = "numeric", L2deriv = "UnivariateDistribution", risk = "asL1", neighbor = "TotalVarNeighborhood"

optimal clipping bound for asymtotic mean absolute error.

clip = "numeric", L2deriv = "UnivariateDistribution", risk = "asL4", neighbor = "ContNeighborhood"

optimal clipping bound for asymtotic mean power 4 error.

clip = "numeric", L2deriv = "UnivariateDistribution", risk = "asL4", neighbor = "TotalVarNeighborhood"

optimal clipping bound for asymtotic mean power 4 error.

clip = "numeric", L2deriv = "UnivariateDistribution", risk = "asUnOvShoot", neighbor = "UncondNeighborhood"

optimal clipping bound for asymtotic under-/overshoot risk.

clip = "numeric", L2deriv = "UnivariateDistribution", risk = "asSemivar", neighbor = "ContNeighborhood"

optimal clipping bound for asymtotic semivariance.

## Author(s)

Peter Ruckdeschel [email protected]

## 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 22, 201-223.

Ruckdeschel, P. (2005) Optimally One-Sided Bounded Influence Curves. Mathematical Methods in Statistics 14(1), 105-131.

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

`ContIC-class`, `TotalVarIC-class`