rlsOptIC.M: Computation of the optimally robust IC for M estimators
In RobLox: Optimally Robust Influence Curves and Estimators for Location and Scale

Description Usage Arguments Details Value Author(s) References See Also Examples

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).

1 2	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)

`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.

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.

Object of class "IC"

Matthias Kohl Matthias.Kohl@stamats.de

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

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

IC-class

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)