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 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*