rlsOptIC.MM2: Computation of the optimally robust IC for MM2 estimators

In RobLox: Optimally Robust Influence Curves and Estimators for Location and Scale

Computation of the optimally robust IC for MM2 estimators

Description

The function rlsOptIC.MM2 computes the optimally robust IC for MM2 estimators in case of normal location with unknown scale and (convex) contamination neighborhoods. These estimators are based on a proposal of Fraiman et al. (2001), p. 206. A definition of these estimators can also be found in Section 8.6 of Kohl (2005).

Usage

rlsOptIC.MM2(r, c.start = 1.5, d.start = 2, delta = 1e-06, MAX = 100)

Arguments

r	non-negative real: neighborhood radius.
c.start	positive real: starting value for c.
d.start	positive real: starting value for d.
delta	the desired accuracy (convergence tolerance).
MAX	if a or k are beyond the admitted values, MAX is returned.

Details

The computation of the optimally robust IC for MM2 estimators is based on optim where MAX is used to control the constraints on c and d. The optimal values of the tuning constants c and d can be read off from the slot Infos of the resulting IC.

Value

Object of class "IC"

Author(s)

Matthias Kohl [e-mail]

References

Fraiman, R., Yohai, V.J. and Zamar, R.H. (2001) Optimal robust M-estimates of location. Ann. Stat. 29(1): 194-223.

M. Kohl (2005). Numerical Contributions to the Asymptotic Theory of Robustness. Dissertation. University of Bayreuth. https://epub.uni-bayreuth.de/id/eprint/839/2/DissMKohl.pdf.

See Also

IC-class

Examples

IC1 <- rlsOptIC.MM2(r = 0.1)
checkIC(IC1)
Risks(IC1)
Infos(IC1)
plot(IC1)
infoPlot(IC1)

RobLox documentation built on Jan. 12, 2025, 3 a.m.