Adaptive estimation of an additive regression function from weakly dependent data

Abstract

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 L2 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.