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
- 62J02 General nonlinear regression

**Résumé:** We study the problem of
estimating some unknown regression function in a
$\beta$-mixing dependent framework.
For this end, we consider some collection of models which
are finite dimensional spaces. A penalized least-squares estimator
(PLSE) is built on a data driven selected model
among this collection. We state non asymptotic risk bounds for this
PLSE and give several examples where our procedure can be applied (autoregression, regression with arithmetically $\beta$-mixing design points, regression with mixing errors, estimation in additive frameworks, estimation of the order of the autoregression ...). In addition we show that under
weak moment condition on the errors, our estimator is adaptive
in the minimax sense simultaneously over some family of Besov balls.

**Mots Clés:** *Nonparametric regression ; Least-squares estimator ; Model selection ; Adaptive estimation ;
Autoregression order ; Additive framework ; Time series ; Mixing processes*

**Date:** 2000-02-17

**Prépublication numéro:** *PMA-566*