Université Paris 6Pierre et Marie Curie Université Paris 7Denis Diderot CNRS U.M.R. 7599 Probabilités et Modèles Aléatoires''

### Random rates in anisotropic regression

Auteur(s):

Code(s) de Classification MSC:

• 62G07 Curve estimation (nonparametric regression, density estimation, etc.)
• 62G10 Hypothesis testing
• 62G15 Tolerance and confidence regions

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