Adaptive estimation of an additive regression function from weakly dependent data

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.Comment: Substantial improvement of the estimator and the main theore

Adaptive estimation of an additive regression function from weakly dependent data

International audienceA d-dimensional nonparametric additive regression model with dependent observa-tions is considered. Using the marginal integration technique and wavelets methodology, we develop a new adaptive estimator for a component of the additive regression func-tion. Its asymptotic properties are investigated via the minimax approach under the 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 i.i.d. case for the standard univariate regression estimation problem