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Uniform in bandwidth consistency of nonparametric regression based on copula representation

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  • Bouzebda, Salim
  • Elhattab, Issam
  • Seck, Cheikh Tidiane

Abstract

We establish in this paper the uniform-in-bandwidth consistency for general kernel-type estimators of regression. More precisely, we investigate the regression estimator based on copula representation. The asymptotic properties are driven by a U-statistic relying on the methods developed in Dony and Mason (2008).

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:137:y:2018:i:c:p:173-182
    DOI: 10.1016/j.spl.2018.01.021
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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. Edward Frees & Emiliano Valdez, 1998. "Understanding Relationships Using Copulas," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 1-25.
    3. David Mason & Jan Swanepoel, 2011. "A general result on the uniform in bandwidth consistency of kernel-type function estimators," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(1), pages 72-94, May.
    4. Paul Deheuvels & David Mason, 2004. "General Asymptotic Confidence Bands Based on Kernel-type Function Estimators," Statistical Inference for Stochastic Processes, Springer, vol. 7(3), pages 225-277, October.
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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. 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.
    3. Salim Bouzebda & Thouria El-hadjali & Anouar Abdeldjaoued Ferfache, 2023. "Uniform in Bandwidth Consistency of Conditional U-statistics Adaptive to Intrinsic Dimension in Presence of Censored Data," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(2), pages 1548-1606, August.

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