Adaptive estimation of an additive regression function from weakly dependent data

Details Adaptive estimation of an additive regression function from weakly dependent data Adaptive estimation of an additive regression function from weakly dependent data

2011-11-16

arxiv.org/abs/1111.3994v1

Mathematics

Statistics Theory

Scientific paper

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.

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