Adaptive estimation of an additive regression function from weakly dependent data

Christophe Chesneau (1) , Jalal M. Fadili (2) , Bertrand Maillot (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme
2 Equipe Image - Laboratoire GREYC - UMR6072

A $d$-dimensional nonparametric additive regression model with dependent observations is considered. Using the marginal integration technique and wavelets methodology, we develop a new adaptive estimator for a component of the additive regression function. Its asymptotic properties are investigated via the minimax approach under the $\mathbb{L}_2$ risk over Besov balls. We prove that it attains a sharp rate of convergence which turns to be the one obtained in the $\iid$ case for the standard univariate regression estimation problem.

Mots clés: Additive regression; Adaptivity; Wavelets; Hard thresholding

Domaines: Théorie [stat.TH]; Statistiques [math.ST]

Christophe Chesneau, Jalal M. Fadili, Bertrand Maillot. Adaptive estimation of an additive regression function from weakly dependent data. 2011. ⟨hal-00641912v2⟩