getRadius: Computation of the Optimal Radius for Given Clipping Bound

In ROptEst: Optimally Robust Estimation

Computation of the Optimal Radius for Given Clipping Bound

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.

Usage

getRadius(IC, risk, neighbor, L2Fam)

Arguments

IC	an IC of class "HampIC".
risk	object of class "RiskType".
neighbor	object of class "Neighborhood".
L2Fam	object of class "L2FamParameter". Can be missing; in this case it is constructed from slot CallL2Fam of IC.

Value

The optimal radius is computed.

Author(s)

Peter Ruckdeschel [e-mail]

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.

See Also

ContIC-class, TotalVarIC-class

Examples

N <- NormLocationFamily(mean=0, sd=1)
nb <- ContNeighborhood(); ri <- asMSE()
radIC <- radiusMinimaxIC(L2Fam=N, neighbor=nb, risk=ri, loRad=0.1, upRad=0.5)
getRadius(radIC, L2Fam=N, neighbor=nb, risk=ri)

## taken from script NormalScaleModel.R in folder scripts
N0 <- NormScaleFamily(mean=0, sd=1)
(N0.IC7 <- radiusMinimaxIC(L2Fam=N0, neighbor=nb, risk=ri, loRad=0, upRad=Inf))
##
getRadius(N0.IC7, risk=asMSE(), neighbor=nb, L2Fam=N0)
getRadius(N0.IC7, risk=asL4(), neighbor=nb, L2Fam=N0)

ROptEst documentation built on Feb. 7, 2024, 3:02 p.m.