Nonasymptotic quasi-optimality of AIC and the slope heuristics in maximum likelihood estimation of density using histogram models

48 p.We consider nonparametric maximum likelihood estimation of density using linear histogram models. More precisely, we investigate optimality of model selection procedures via penalization, when the number of models is polynomial in the number of data. It turns out that the Slope Heuristics rst formulated by Birgé and Massart [10] is satised under rather mild conditions on the density to be estimated and the structure of the considered partitions, and that the minimal penalty is equivalent to half of AIC penalty