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Adaptive estimation of an additive regression function from weakly dependent data

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  • Chesneau, Christophe
  • Fadili, Jalal
  • Maillot, Bertrand

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.

Suggested Citation

  • Chesneau, Christophe & Fadili, Jalal & Maillot, Bertrand, 2015. "Adaptive estimation of an additive regression function from weakly dependent data," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 77-94.
    • Handle: RePEc:eee:jmvana:v:133:y:2015:i:c:p:77-94
    DOI: 10.1016/j.jmva.2014.09.005
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    References listed on IDEAS

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    Cited by:

    1. Joseph Ngatchou-Wandji & Marwa Ltaifa & Didier Alain Njamen Njomen & Jia Shen, 2022. "Nonparametric Estimation of the Density Function of the Distribution of the Noise in CHARN Models," Mathematics, MDPI, vol. 10(4), pages 1-20, February.
    2. Huijun Guo & Youming Liu, 2019. "Regression estimation under strong mixing data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(3), pages 553-576, June.
    3. Christophe Chesneau & Fabien Navarro, 2017. "On the pointwise mean squared error of a multidimensional term-by-term thresholding wavelet estimator," Working Papers 2017-68, Center for Research in Economics and Statistics.
    4. Junke Kou & Youming Liu, 2018. "Wavelet regression estimations with strong mixing data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(4), pages 667-688, December.

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