RobLox (version 1.2.3)

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

Description

The function rlsOptIC.M computes the optimally robust IC for M estimators in case of normal location with unknown scale and (convex) contamination neighborhoods. The definition of these estimators can be found in Section 8.3 of Kohl (2005).

Usage

rlsOptIC.M(r, ggLo = 0.5, ggUp = 1.5, a1.start = 0.75, a3.start = 0.25, 
           bUp = 1000, delta = 1e-05, itmax = 100, check = FALSE)

Value

Object of class "IC"

Arguments

r

non-negative real: neighborhood radius.

ggLo

non-negative real: the lower end point of the interval to be searched for \(\gamma\).

ggUp

positive real: the upper end point of the interval to be searched for \(\gamma\).

a1.start

real: starting value for \(\alpha_1\).

a3.start

real: starting value for \(\alpha_3\).

bUp

positive real: upper bound used in the computation of the optimal clipping bound b.

delta

the desired accuracy (convergence tolerance).

itmax

the maximum number of iterations.

check

logical. Should constraints be checked.

Author

Matthias Kohl

Details

The optimal values of the tuning constants \(\alpha_1\), \(\alpha_3\), b and \(\gamma\) can be read off from the slot Infos of the resulting IC.

References

Huber, P.J. (1981) Robust Statistics. New York: Wiley.

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.M(r = 0.1, check = TRUE)
distrExOptions("ErelativeTolerance" = 1e-12)
checkIC(IC1, NormLocationScaleFamily())
distrExOptions("ErelativeTolerance" = .Machine$double.eps^0.25)
Risks(IC1)
Infos(IC1)
plot(IC1)
infoPlot(IC1)