Hi list, 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.) 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? Thank you, Christian *** NEW ADDRESS! *** Christian Hennig University College London, Department of Statistical Science Gower St., London WC1E 6BT, phone +44 207 679 1698 chrish at stats.ucl.ac.uk, www.homepages.ucl.ac.uk/~ucakche
Christian Hennig wrote:>Hi list, > >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 done this once, but cannot find the code or remember the constant. But given the constant, it is easy to do this in R. rlm has an argument psi with default psi huber: > psi.huber function (u, k = 1.345, deriv = 0) { if (!deriv) return(pmin(1, k/abs(u))) abs(u) <= k } <environment: namespace:MASS> Use this argument with psi=function(u, k= your.value, deriv=0) psi.huber(u,k,deriv)>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?) >Not sure about this at the moment.> Or what else? What does "rescaled" mean? > >"rescaled" means multiplied with the constant which makes it a consistent estimator under the normal model, default in the R mad function Kjetil>Thank you, >Christian > > >*** NEW ADDRESS! *** >Christian Hennig >University College London, Department of Statistical Science >Gower St., London WC1E 6BT, phone +44 207 679 1698 >chrish at stats.ucl.ac.uk, www.homepages.ucl.ac.uk/~ucakche > >______________________________________________ >R-help at stat.math.ethz.ch mailing list >https://stat.ethz.ch/mailman/listinfo/r-help >PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html > > > > >-- Kjetil Halvorsen. Peace is the most effective weapon of mass construction. -- Mahdi Elmandjra -- No virus found in this outgoing message. Checked by AVG Anti-Virus.
Christian Hennig wrote:>Hi list, > >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.) > >Hi Christian, 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). See: http://mathstat.math.carleton.ca:16080/~matias/thesis.pdf 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! Matthias>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? > >Thank you, >Christian > > >*** NEW ADDRESS! *** >Christian Hennig >University College London, Department of Statistical Science >Gower St., London WC1E 6BT, phone +44 207 679 1698 >chrish at stats.ucl.ac.uk, www.homepages.ucl.ac.uk/~ucakche > >______________________________________________ >R-help at stat.math.ethz.ch mailing list >https://stat.ethz.ch/mailman/listinfo/r-help >PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html > >