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Bandwidth Selection for Recursive Kernel Density Estimators Defined by Stochastic Approximation Method

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  • Yousri Slaoui

Abstract

We propose an automatic selection of the bandwidth of the recursive kernel estimators of a probability density function defined by the stochastic approximation algorithm introduced by Mokkadem et al. (2009a). We showed that, using the selected bandwidth and the stepsize which minimize the MISE (mean integrated squared error) of the class of the recursive estimators defined in Mokkadem et al. (2009a), the recursive estimator will be better than the nonrecursive one for small sample setting in terms of estimation error and computational costs. We corroborated these theoretical results through simulation study.

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  • 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.
    • Handle: RePEc:hin:jnljps:739640
    DOI: 10.1155/2014/739640
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    Cited by:

    1. Bouzebda, Salim & Slaoui, Yousri, 2022. "Nonparametric recursive method for moment generating function kernel-type estimators," Statistics & Probability Letters, Elsevier, vol. 184(C).
    2. Timothy Fortune & Hailin Sang, 2020. "Shannon Entropy Estimation for Linear Processes," JRFM, MDPI, vol. 13(9), pages 1-13, September.
    3. 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.
    4. Slaoui Yousri & Khardani Salah, 2020. "Nonparametric relative recursive regression," Dependence Modeling, De Gruyter, vol. 8(1), pages 221-238, January.
    5. Slaoui Yousri & Khardani Salah, 2020. "Nonparametric relative recursive regression," Dependence Modeling, De Gruyter, vol. 8(1), pages 221-238, January.
    6. Ariane Hanebeck & Bernhard Klar, 2021. "Smooth distribution function estimation for lifetime distributions using Szasz–Mirakyan operators," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(6), pages 1229-1247, December.
    7. Wu, Yi & Yu, Wei & Wang, Xuejun & Shen, Aiting, 2021. "The rate of complete consistency for recursive probability density estimator under strong mixing samples," Statistics & Probability Letters, Elsevier, vol. 176(C).
    8. Slaoui Yousri, 2019. "Optimal bandwidth selection for recursive Gumbel kernel density estimators," Dependence Modeling, De Gruyter, vol. 7(1), pages 375-393, January.

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