# 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).

### Usage

```lowerCaseRadius(L2Fam, neighbor, risk, biastype, ...)
```

### 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.

`L2ParamFamily-class`, `Neighborhood-class`
```lowerCaseRadius(BinomFamily(size = 10), ContNeighborhood(), asMSE())