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Consistency of the recursive nonparametric regression estimation for dependent functional data

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  • Aboubacar Amiri
  • Baba Thiam

Abstract

We consider the recursive estimation of a regression functional where the explanatory variables take values in some functional space. We prove the almost sure convergence of such estimates for dependent functional data. Also we derive the mean quadratic error of the considered class of estimators. Our results are established with rates and asymptotic appear bounds, under strong mixing condition. Finally, the feasibility of the proposed estimator is illustrated throughout an empirical study.

Suggested Citation

  • Aboubacar Amiri & Baba Thiam, 2014. "Consistency of the recursive nonparametric regression estimation for dependent functional data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(3), pages 471-487, September.
    • Handle: RePEc:taf:gnstxx:v:26:y:2014:i:3:p:471-487
    DOI: 10.1080/10485252.2014.907406
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    Cited by:

    1. Said Attaoui & Nengxiang Ling, 2016. "Asymptotic results of a nonparametric conditional cumulative distribution estimator in the single functional index modeling for time series data with applications," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(5), pages 485-511, July.
    2. 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.

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