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The rate of complete consistency for recursive probability density estimator under strong mixing samples

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  • Wu, Yi
  • Yu, Wei
  • Wang, Xuejun
  • Shen, Aiting

Abstract

In this paper, we mainly study the recursive density estimators of the probability density function for strong mixing random variables. The rate of complete consistency is established under some suitable conditions. As an application, we further investigate the rate of complete consistency for hazard rate function estimator. We also present some numerical studies to verify the validity of our theoretical results.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:stapro:v:176:y:2021:i:c:s0167715221000924
    DOI: 10.1016/j.spl.2021.109130
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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. Han-Ying Liang & Jong-Il Baek, 2004. "Asymptotic normality of recursive density estimates under some dependence assumptions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 60(2), pages 155-166, September.
    3. Lanh Tran, 1990. "Recursive kernel density estimators under a weak dependence condition," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(2), pages 305-329, June.
    4. Liebscher E., 2001. "Estimation Of The Density And The Regression Function Under Mixing Conditions," Statistics & Risk Modeling, De Gruyter, vol. 19(1), pages 9-26, January.
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