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

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

Adaptive prediction and estimation in linear regression with infinitely many parameters

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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