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

### Optimal prediction for linear regression with infinitely many parameters

Auteur(s):

Code(s) de Classification MSC:

• 62G05 Estimation
• 62G20 Asymptotic properties

Résumé: The problem of optimal prediction in the stochastic linear regression model with infinitely many parameters is considered. We suggest a prediction method that is asymptotically minimax over ellipsoids in $\ell_2$. The method is based on a regularized least squares estimator with weights of the Pinsker filter. We also consider the case of dynamic linear regression which is important in the context of transfer function modeling.

Mots Clés: Linear regression with infinitely many parameters ; optimal prediction ; exact asymptotics of minimax risk ; Pinsker filter

Date: 1999-11-17

Prépublication numéro: PMA-541