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

CNRS U.M.R. 7599
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``Probabilités et Modèles Aléatoires''
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**Auteur(s): **

**Code(s) de Classification MSC:**

- 62G05 Estimation
- 62G20 Asymptotic properties

**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