Adaptive estimation of an additive regression function from weakly dependent data
Résumé
A $d$-dimensional nonparametric additive regression model with dependent observations is considered. Using the marginal integration and the methods of wavelets, 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, close to the one obtained in the one-dimensional case. In particular, it is both independent of $d$ and slightly deteriorated by the dependence of the observations.
Origine : Fichiers produits par l'(les) auteur(s)