[R] rlm/M/MM-estimator questions
Matthias.Kohl at uni-bayreuth.de
Thu Jul 7 09:49:03 CEST 2005
Christian Hennig wrote:
>1) How can the MM-estimator method="MM" in function rlm be tuned to 85%
>efficiency? It seems that there is a default tuning to 95%. I presume, but
>am not sure, that the MM-estimator uses phi=phi.bisquare as default and
>the tuning constant could be set by adding a parameter c=...
>Is this true? Which value to use for 85%?
>(In principle I should be able to figure that out theoretically, but it
>would be much easier if somebody already knew the constant or a
>straightforward way to compute it.)
I have not calculated the efficiency myself ...
But the thesis of Matias Salibian-Barrera (SB 2000) might help you to
find the answer
(cf. Chapter 4).
As far as I understand the choice k0=1.548 is to obtain a breakdown
point 0.5 whereas k0=1.988 leads to a breakdown point of 0.4 - at least
in the location case; confer p. 60 of SB 2000.
In the article "Optimal robust $M$-estimates of location" by Fraiman,
Yohai and Zamar (Ann. Stat. 29(1): 194 - 223) which is, of course,
concerned with the location case, the authors recommend to use k0=1.988
instead of k0=1.548 (cf. p. 206).
Hope that helps!
>2) The M-estimator with bisquare uses "rescaled MAD of the residuals" as
>scale estimator according to the rlm help page. Does this mean that a
>scale estimator is used which is computed from least squares residuals? Are
>M-estimator and residual scale estimator iterated until convergence of
>them both? (Does this converge?) Or what else? What does "rescaled" mean?
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