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

Value

lower case radius

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 [e-mail], Peter Ruckdeschel [e-mail]

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.

See Also

L2ParamFamily-class, Neighborhood-class

Examples

lowerCaseRadius(BinomFamily(size = 10), ContNeighborhood(), asMSE())
lowerCaseRadius(BinomFamily(size = 10), TotalVarNeighborhood(), asMSE())

ROptEst documentation built on Sept. 12, 2024, 7:40 a.m.