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Recursive nonparametric regression estimation for dependent strong mixing functional data

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  • Yousri Slaoui

    (Univ. Poitiers)

Abstract

In the present paper, we extend the work of Slaoui (Stat Sin 30:417–437, 2020) in the case of strong mixing data. Since, we are interested in nonparametric regression estimation, we focus on well adapted dependence structures based on mixing type conditions. We study the properties of these regression estimators and compare them with the nonparametric non-recursive regression estimator. The bias, variance and mean squared error are computed explicitly. We showed that using a selected wild bootstrap bandwidth procedure and a special stepsize, our proposed recursive regression estimators allowed us to obtain quite similar results compared to the non-recursive regression estimator under $$\alpha $$ α -mixing condition in terms of estimation error and much better in terms of computational costs.

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  • Yousri Slaoui, 2020. "Recursive nonparametric regression estimation for dependent strong mixing functional data," Statistical Inference for Stochastic Processes, Springer, vol. 23(3), pages 665-697, October.
    • Handle: RePEc:spr:sistpr:v:23:y:2020:i:3:d:10.1007_s11203-020-09223-3
    DOI: 10.1007/s11203-020-09223-3
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    Cited by:

    1. Salim Bouzebda & Yousri Slaoui, 2023. "Nonparametric Recursive Estimation for Multivariate Derivative Functions by Stochastic Approximation Method," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 658-690, February.
    2. Fatimah Alshahrani & Ibrahim M. Almanjahie & Zouaoui Chikr Elmezouar & Zoulikha Kaid & Ali Laksaci & Mustapha Rachdi, 2022. "Functional Ergodic Time Series Analysis Using Expectile Regression," Mathematics, MDPI, vol. 10(20), pages 1-17, October.

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