rlsOptIC.BM {RobLox}

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)

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.

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.

Value

Object of class "IC"

Author(s)

Matthias Kohl [e-mail]

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. 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)