Maximum likelihood estimation for Tukey's three corners

We use the EM algorithm to derive recursive expressions for maximum likelihood location and scale estimators for Tukey's corner distributions, in particular the one-wild. This now enables optimal estimation for the triefficiency criterion used to appraise robust estimators. The effect of improved estimation for the one-wild case is investigated. Simulations are conducted, both to illustrate the operation of the algorithm, and to reinvestigate the properties of three common location estimates. In particular, the scaling constant c = 6 in the one-step biweight M-estimator used in procedures such as loess, is shown to be too small under the triefficiency criterion. (C) 2003 Elsevier B.V. All rights reserved.