| Université Paris 6 Pierre et Marie Curie | Université Paris 7 Denis Diderot | |
| CNRS U.M.R. 7599 | ||
| ``Probabilités et Modèles Aléatoires'' | ||
Auteur(s):
Code(s) de Classification MSC:
Résumé: We consider the gaussian sequence space model. Using a penalized blockwise Stein's rule with an appropriate choice of blocks and respective penalties, we construct a nonlinear estimator that enjoys simultaneously the following properties: (i) it satisfies asymptotically exact oracle inequalities within any class of linear estimates having monotone non-decreasing weights,(ii) it is sharp asymptotically minimax on any ellipsoid in $\ell_2$ with monotone non-decreasing coefficients, (iii) it is almost sharp asymptotically minimax on other bodies such as hyperrectangles, tail-classes, Besov classes with $p\ge 2$, (iv) it attains the optimal rate of convergence (up to a log-factor) on the Besov classes with $p<2$. A surprising fact is that there exists a large variety of estimators that possess these four properties simultaneously.
Mots Clés: Adaptive curve estimation ; Exact minimax constants ; Oracle inequalities ; Monotone oracle ; Penalized blockwise Stein's rule
Date: 2001-09-27
Prépublication numéro: PMA-689
Postscript file : PMA-689.ps