The "progressive mixture" estimator for regression trees

We present a version of O. Catoni's "progressive mixture estimator" (1999) suited for a general regression framework. Following basically Catoni's ste ps, we derive strong non-asymptotic upper bounds for the Kullback-Leibler r isk in this framework. We give a more explicit form for this bound when the models considered are regression trees, present a modified version of the estimator in an extended framework and propose an approximate computation u sing a Metropolis algorithm. (C) Elsevier, Paris.