RobLox (version 1.2.3)

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

Description

The function rlsOptIC.BM computes the optimally robust IC for BM estimators in case of normal location with unknown scale and (convex) contamination neighborhoods. These estimators were proposed by Bednarski and Mueller (2001). A definition of these estimators can also be found in Section 8.4 of Kohl (2005).

Usage

rlsOptIC.BM(r, bL.start = 2, bS.start = 1.5, delta = 1e-06, MAX = 100)

Value

Object of class "IC"

Arguments

r

non-negative real: neighborhood radius.

bL.start

positive real: starting value for \(b_{\rm loc}\).

bS.start

positive real: starting value for \(b_{{\rm sc},0}\).

delta

the desired accuracy (convergence tolerance).

MAX

if \(b_{\rm loc}\) or \(b_{{\rm sc},0}\) are beyond the admitted values, MAX is returned.

Author

Matthias Kohl

Details

The computation of the optimally robust IC for BM estimators is based on optim where MAX is used to control the constraints on \(b_{\rm loc}\) and \(b_{{\rm sc},0}\). The optimal values of the tuning constants \(b_{\rm loc}\), \(b_{{\rm sc},0}\), \(\alpha\) and \(\gamma\) can be read off from the slot Infos of the resulting IC.

References

Bednarski, T and Mueller, C.H. (2001) Optimal bounded influence regression and scale M-estimators in the context of experimental design. Statistics, 35(4): 349-369.

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.

M. Kohl (2012). Bounded influence estimation for regression and scale. Statistics, 46(4): 437-488. tools:::Rd_expr_doi("10.1080/02331888.2010.540668")

See Also

IC-class

Examples

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