Adaptive estimation of an additive regression function from weakly dependent data

2011/11/16 by Christophe Chesneau, Chesneau, Christophe, Jalal M. Fadili +3
Mathematics · #FOS: Mathematics #Statistics Theory (math.ST) #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.1111.3994

Substantial improvement of the estimator and the main theorem

arxiv created 2012/08/06 · arxiv updated 2012/08/07

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 \mathbbL₂ 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.

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