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Complete convergence for weighted sums of END random variables and its application to nonparametric regression models

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  • Aiting Shen

Abstract

In this article, the complete convergence for weighted sums of extended negatively dependent (END, for short) random variables is investigated. Some sufficient conditions for the complete convergence are provided. In addition, the Marcinkiewicz–Zygmund type strong law of large numbers for weighted sums of END random variables is obtained. The results obtained in the article generalise and improve the corresponding one of Wang et al. [(2014b), ‘On Complete Convergence for an Extended Negatively Dependent Sequence’, Communications in Statistics-Theory and Methods, 43, 2923–2937]. As an application, the complete consistency for the estimator of nonparametric regression model is established.

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  • Aiting Shen, 2016. "Complete convergence for weighted sums of END random variables and its application to nonparametric regression models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(4), pages 702-715, October.
    • Handle: RePEc:taf:gnstxx:v:28:y:2016:i:4:p:702-715
    DOI: 10.1080/10485252.2016.1225050
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    Cited by:

    1. Yi Wu & Xuejun Wang & Aiting Shen, 2021. "Strong convergence properties for weighted sums of m-asymptotic negatively associated random variables and statistical applications," Statistical Papers, Springer, vol. 62(5), pages 2169-2194, October.
    2. Xuejun Wang & Yi Wu & Shuhe Hu, 2019. "The Berry–Esseen bounds of the weighted estimator in a nonparametric regression model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(5), pages 1143-1162, October.
    3. Yan Wang & Xuejun Wang, 2021. "Complete f-moment convergence for Sung’s type weighted sums and its application to the EV regression models," Statistical Papers, Springer, vol. 62(2), pages 769-793, April.
    4. Yi Wu & Xuejun Wang & Aiting Shen, 2023. "Strong Convergence for Weighted Sums of Widely Orthant Dependent Random Variables and Applications," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-28, March.
    5. Xin Deng & Xuejun Wang & Yi Wu, 2021. "The Berry–Esseen type bounds of the weighted estimator in a nonparametric model with linear process errors," Statistical Papers, Springer, vol. 62(2), pages 963-984, April.
    6. Liangxue Li & Xiaoqian Zheng & Haiwu Huang & Xuejun Wang, 2024. "Strong Convergence Properties for Weighted Sums of Extended Negatively Dependent Random Variables Under Sub-linear Expectations with Statistical Applications," Methodology and Computing in Applied Probability, Springer, vol. 26(3), pages 1-36, September.
    7. Yan, Ji Gao, 2018. "On Complete Convergence in Marcinkiewicz-Zygmund Type SLLN for END Random Variables and its Applications," IRTG 1792 Discussion Papers 2018-042, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".

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