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Optimal bandwidth selection for recursive Gumbel kernel density estimators

Author

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  • Slaoui Yousri

    (Université de Poitiers)

Abstract

In this paper, we propose a data driven bandwidth selection of the recursive Gumbel kernel estimators of a probability density function based on a stochastic approximation algorithm. The choice of the bandwidth selection approaches is investigated by a second generation plug-in method. Convergence properties of the proposed recursive Gumbel kernel estimators are established. The uniform strong consistency of the proposed recursive Gumbel kernel estimators is derived. The new recursive Gumbel kernel estimators are compared to the non-recursive Gumbel kernel estimator and the performance of the two estimators are illustrated via simulations as well as a real application.

Suggested Citation

  • Slaoui Yousri, 2019. "Optimal bandwidth selection for recursive Gumbel kernel density estimators," Dependence Modeling, De Gruyter, vol. 7(1), pages 375-393, January.
    • Handle: RePEc:vrs:demode:v:7:y:2019:i:1:p:375-393:n:20
    DOI: 10.1515/demo-2019-0020
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    References listed on IDEAS

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    1. Yousri Slaoui, 2014. "Bandwidth Selection for Recursive Kernel Density Estimators Defined by Stochastic Approximation Method," Journal of Probability and Statistics, Hindawi, vol. 2014, pages 1-11, June.
    2. Yousri Slaoui, 2018. "Bias reduction in kernel density estimation," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 30(2), pages 505-522, April.
    3. Felipe Gusmão & Edwin Ortega & Gauss Cordeiro, 2011. "The generalized inverse Weibull distribution," Statistical Papers, Springer, vol. 52(3), pages 591-619, August.
    4. Delaigle, A. & Gijbels, I., 2004. "Practical bandwidth selection in deconvolution kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 249-267, March.
    5. 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.
    6. B. Béranger & T. Duong & S. E. Perkins-Kirkpatrick & S. A. Sisson, 2019. "Tail density estimation for exploratory data analysis using kernel methods," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 31(1), pages 144-174, January.
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