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

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

Random rates in anisotropic regression


Code(s) de Classification MSC:

Résumé: In the context of the minimax theory, we propose a new kind of risk, normalized by a random variable, measurable with respect to the data. We present a notion of optimality and a method to construct optimal procedures accordingly. We apply this general setup to the problem of searching for significant variables in Gaussian white noise. In particular, we show that our method essentially improves the {\it accuracy of estimation}, in the sense of giving explicit (random) improved confidence intervals in $L_2$-norm. Links to adaptive estimation are discussed.

Mots Clés: nonparametric estimation ; minimax theory ; random normalizing factors ; anisotropic regression

Date: 2000-02-18

Prépublication numéro: PMA-568