Adaptive estimation of an additive regression function from weakly dependent data

JOURNAL OF MULTIVARIATE ANALYSIS

卷:133

Article

Chesneau, Christophe¹  Fadili, Jalal²  Maillot, Bertrand¹ 

[1] Univ Caen, LMNO, CNRS, F-14032 Caen, France

[2] Univ Caen, GREYC, CNRS, ENSICAEN, F-14032 Caen, France

关键词: Additive regression;    Dependent data;    Adaptivity;    Wavelets;    Hard thresholding;   

DOI  :  10.1016/j.jmva.2014.09.005

来源: Elsevier

【 摘 要 】

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 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. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free