# lowerCaseRadius: Computation of the lower case radius In ROptEst: Optimally Robust Estimation

## Computation of the lower case radius

### Description

The lower case radius is computed; confer Subsection 2.1.2 in Kohl (2005) and formula (4.5) in Ruckdeschel (2005).

### Arguments

 L2Fam L2 differentiable parametric family neighbor object of class "Neighborhood" risk object of class "RiskType" biastype object of class "BiasType" ... additional parameters

### Methods

L2Fam = "L2ParamFamily", neighbor = "ContNeighborhood", risk = "asMSE", biastype = "BiasType"

lower case radius for risk "asMSE" in case of "ContNeighborhood" for symmetric bias.

L2Fam = "L2ParamFamily", neighbor = "TotalVarNeighborhood", risk = "asMSE", biastype = "BiasType"

lower case radius for risk "asMSE" in case of "TotalVarNeighborhood"; (argument biastype is just for signature reasons).

L2Fam = "L2ParamFamily", neighbor = "ContNeighborhood", risk = "asMSE", biastype = "onesidedBias"

lower case radius for risk "asMSE" in case of "ContNeighborhood" for onesided bias.

L2Fam = "L2ParamFamily", neighbor = "ContNeighborhood", risk = "asMSE", biastype = "asymmetricBias"

lower case radius for risk "asMSE" in case of "ContNeighborhood" for asymmetric bias.

L2Fam = "UnivariateDistribution", neighbor = "ContNeighborhood", risk = "asMSE", biastype = "onesidedBias"

used only internally; trick to be able to call lower case radius from within minmax bias solver

### Author(s)

Matthias Kohl Matthias.Kohl@stamats.de, Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

### References

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

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