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Nonparametric Recursive Method for Generalized Kernel Estimators for Dependent Functional Data

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  • Yousri Slaoui

    (Univ. Poitiers, Lab. Math. et Appl.)

Abstract

In the present paper, we are concerned with a generalized kernel estimators defined by the stochastic approximation algorithm in the case of dependent functional data. We establish the central limit theorem for the proposed estimators under some mild conditions. We then approach the distribution of the bias distribution of our estimate by the bootstrapped distribution when it is conditioned by the data using the Kolmogorov distance.

Suggested Citation

  • Yousri Slaoui, 2024. "Nonparametric Recursive Method for Generalized Kernel Estimators for Dependent Functional Data," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 86(1), pages 392-430, February.
    • Handle: RePEc:spr:sankha:v:86:y:2024:i:1:d:10.1007_s13171-023-00325-7
    DOI: 10.1007/s13171-023-00325-7
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    References listed on IDEAS

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    8. 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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    16. Asma Jmaei & Yousri Slaoui & Wassima Dellagi, 2017. "Recursive distribution estimator defined by stochastic approximation method using Bernstein polynomials," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(4), pages 792-805, October.
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