RobLox (version 0.8.2)

rlsOptIC.HaMad: Computation of the optimally robust IC for HuMad estimators

Description

The function rlsOptIC.HuMad computes the optimally robust IC for HuMad estimators in case of normal location with unknown scale and (convex) contamination neighborhoods. These estimators were considered in Andrews et al. (1972). A definition of these estimators can also be found in Subsection 8.5.2 of Kohl (2005).

Usage

rlsOptIC.HaMad(r, a.start = 0.25, b.start = 2.5, c.start = 5, 
               delta = 1e-06, MAX = 100)

Arguments

r

non-negative real: neighborhood radius.

a.start

positive real: starting value for a.

b.start

positive real: starting value for b.

c.start

positive real: starting value for c.

delta

the desired accuracy (convergence tolerance).

MAX

if a or b or c are beyond the admitted values, MAX is returned.

Value

• Object of class "IC"

concept

• normal location and scale
• influence curve

Details

The computation of the optimally robust IC for HaMad estimators is based on optim where MAX is used to control the constraints on a, b and c. The optimal values of the tuning constants a, b, and c can be read off from the slot Infos of the resulting IC.

References

Andrews, D.F., Bickel, P.J., Hampel, F.R., Huber, P.J., Rogers, W.H. and Tukey, J.W. (1972) Robust estimates of location. Princeton University Press. Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

IC-class

Examples

IC1 <- rlsOptIC.HaMad(r = 0.1)
checkIC(IC1)
Risks(IC1)
Infos(IC1)
plot(IC1)
infoPlot(IC1)