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

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

Adaptive density estimation using Stein's blockwise method


Code(s) de Classification MSC:

Résumé: We study the problem of nonparametric estimation of a probability density of unknown smoothness in $L_2(\R)$. Expressing mean integrated squared error in the Fourier domain, we show that it is close to mean squared error in the Gaussian sequence model. Then applying a modified version of Stein's blockwise method, we obtain a linear monotone oracle inequality. As a consequence, we show that the proposed estimator is sharp minimax adaptive on a scale of Sobolev classes of densities. Simulations in classical cases are also provided and confirm a good performance of the estimator for a finite number of observations.

Mots Clés: Adaptive density estimation ; Blockwise Stein's rule ; Exact minimax constants ; Kernel oracle ; Oracle inequalities ; Monotone oracle

Date: 2004-05-13

Prépublication numéro: PMA-913