• O. CATONI

Code(s) de Classification MSC:

• 62G07 Curve estimation (nonparametric regression, density estimation, etc.)
• 62F35 Robustness and adaptive procedures
• 62F11 Small sample properties of estimators
• 94A45 Prefix, length-variable, comma-free codes, See also {20M35,

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