Histograms selection with an Akaike type criterion

We address the problem of choosing a histogram estimator from a sample of some unknown density. We consider regular as well as irregular partitions and propose a penalized maximum likelihood selection criterion. We define the penalty term involved in our criterion in order to minimize non asymptotically the Hellinger risk for the resulting penalized estimator. Our criterion appears either as a mild correction or as a substantial modification of Akaike's criterion, depending on the complexity of the collection of partitions to be considered (C) 2000 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.