| 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: The problem of adaptive prediction and estimation in the stochastic linear regression model with infinitely many parameters is considered. We suggest a prediction method that is sharp asymptotically minimax adaptive over ellipsoids in $\ell_2$. The method consists in an application of blockwise Stein's rule with ``weakly'' geometrically increasing blocks to the penalized least squares fits of the first $N$ coefficients. To prove the results we develop oracle inequalities for sequence model with correlated data.
Mots Clés: Linear regression with infinitely many parameters ; adaptive prediction ; exact asymptotics of minimax risk ;
blockwise Stein's rule ; oracle inequalities
Date: 2000-06-07
Prépublication numéro: PMA-598
Postscript file : PMA-598.ps