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Nonparametric recursive method for kernel-type function estimators for spatial data

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  • Bouzebda, Salim
  • Slaoui, Yousri

Abstract

In the present paper we propose recursive general kernel-type estimators for spatial data defined by the stochastic approximation algorithm. We obtain the central limit theorem and strong pointwise convergence rate for the nonparametric recursive general kernel-type estimators under some mild conditions. Finally, we investigate the MISE of the proposed estimators and provide the optimal bandwidth.

Suggested Citation

  • Bouzebda, Salim & Slaoui, Yousri, 2018. "Nonparametric recursive method for kernel-type function estimators for spatial data," Statistics & Probability Letters, Elsevier, vol. 139(C), pages 103-114.
    • Handle: RePEc:eee:stapro:v:139:y:2018:i:c:p:103-114
    DOI: 10.1016/j.spl.2018.03.017
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    References listed on IDEAS

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    1. David Mason, 2012. "Proving consistency of non-standard kernel estimators," Statistical Inference for Stochastic Processes, Springer, vol. 15(2), pages 151-176, July.
    2. Bouzebda, Salim & Elhattab, Issam & Seck, Cheikh Tidiane, 2018. "Uniform in bandwidth consistency of nonparametric regression based on copula representation," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 173-182.
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    Cited by:

    1. Bouzebda, Salim & Slaoui, Yousri, 2019. "Large and moderate deviation principles for recursive kernel estimators of a regression function for spatial data defined by stochastic approximation method," Statistics & Probability Letters, Elsevier, vol. 151(C), pages 17-28.

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