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Recursive regression estimation based on the two-time-scale stochastic approximation method and Bernstein polynomials

Author

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  • Slaoui Yousri

    (Laboratoire de Mathématiques et Applications, UMR 7348 du CNRS Site du Futuroscope, Université de Poitiers, Téléport 2, Bâtiment H3 11 Bd Marie et Pierre Curie, 86073Poitierscedex 9, France)

  • Helali Salima

    (Laboratoire Angevin de Recherche en Mathématiques, Faculté des Sciences Bâtiment I, Université d’Angers, 2 Boulevard Lavoisier 49045Angerscedex 01, France)

Abstract

In this paper, we propose a recursive estimators of the regression function based on the two-time-scale stochastic approximation algorithms and the Bernstein polynomials. We study the asymptotic properties of this estimators. We compare the proposed estimators with the classic regression estimator using the Bernstein polynomial defined by Tenbusch. Results showed that, our proposed recursive estimators can overcome the problem of the edges associated with kernel regression estimation with a compact support. The proposed recursive two-time-scale estimators are compared to the non-recursive estimator introduced by Tenbusch and the performance of the two estimators are illustrated via simulations as well as two real datasets.

Suggested Citation

  • Slaoui Yousri & Helali Salima, 2022. "Recursive regression estimation based on the two-time-scale stochastic approximation method and Bernstein polynomials," Monte Carlo Methods and Applications, De Gruyter, vol. 28(1), pages 45-59, March.
    • Handle: RePEc:bpj:mcmeap:v:28:y:2022:i:1:p:45-59:n:1
    DOI: 10.1515/mcma-2022-2104
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