ROptEst (version 1.3.4)

lowerCaseRadius: 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, ...)

Value

lower case radius

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

Matthias Kohl , Peter Ruckdeschel

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())