Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

Data compression and adaptive histograms


Code(s) de Classification MSC:

Résumé: We describe and study in this paper a two step estimation scheme for density estimation from i.i.d. observations. Each step is based on the Gibbs aggregation rule and computes an adaptive histogram for which a non asymptotic oracle inequality is satisfied. The estimator computed in the first step is used to code the data in the unit interval in a way that is inspired by arithmetic coding. The second estimator analyzes the coded sample and refines the first one. Numerical evidences are provided of the efficiency of the method.

Mots Clés: Density estimation ; adaptive histograms ; Kullback Leibler divergence ; data compression

Date: 2000-09-06

Prépublication numéro: PMA-609

Postscript file : PMA-609.ps

Revised version : PMA-609bis.ps