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

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

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)

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.

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.

Value

Object of class "IC"

Author(s)

Matthias Kohl [e-mail]

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)

RobLox documentation built on Sept. 5, 2024, 3 a.m.