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Complete f-moment convergence for Sung’s type weighted sums and its application to the EV regression models

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  • Yan Wang

    (Anhui University)

  • Xuejun Wang

    (Anhui University)

Abstract

In this paper, we establish a general result on the complete f-moment convergence for Sung’s type weighted sums of extended negatively dependent random variables under some general assumptions. As applications, we investigate the strong consistency of the least square estimator in the simple linear errors-in-variables models, and provide some simulations to verify the validity of our theoretical results.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stpapr:v:62:y:2021:i:2:d:10.1007_s00362-019-01112-z
    DOI: 10.1007/s00362-019-01112-z
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    References listed on IDEAS

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    1. Yu Miao & Fangfang Zhao & Ke Wang & Yanping Chen, 2013. "Asymptotic normality and strong consistency of LS estimators in the EV regression model with NA errors," Statistical Papers, Springer, vol. 54(1), pages 193-206, February.
    2. Xuejun Wang & Aiting Shen & Zhiyong Chen & Shuhe Hu, 2015. "Complete convergence for weighted sums of NSD random variables and its application in the EV regression model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(1), pages 166-184, March.
    3. Miao, Yu & Wang, Ke & Zhao, Fangfang, 2011. "Some limit behaviors for the LS estimator in simple linear EV regression models," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 92-102, January.
    4. Aiting Shen & Mingxiang Xue & Wenjuan Wang, 2017. "Complete convergence for weighted sums of extended negatively dependent random variables," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(3), pages 1433-1444, February.
    5. Dawei Lu & Lixin Song & Xiaohu Wang, 2016. "Precise large deviation for the difference of two sums of random variables," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(2), pages 291-306, January.
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    8. 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.
    9. Andre Adler & Andrew Rosalsky & Robert L. Taylor, 1989. "Strong laws of large numbers for weighted sums of random elements in normed linear spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 12, pages 1-23, January.
    10. Wenzhi Yang & Haiyun Xu & Ling Chen & Shuhe Hu, 2018. "Complete consistency of estimators for regression models based on extended negatively dependent errors," Statistical Papers, Springer, vol. 59(2), pages 449-465, June.
    11. Yi Wu & Xuejun Wang & Shuhe Hu & Lianqiang Yang, 2018. "Weighted version of strong law of large numbers for a class of random variables and its applications," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(2), pages 379-406, June.
    12. Di Hu & Pingyan Chen & Soo Hak Sung, 2017. "Strong laws for weighted sums of $$\psi $$ ψ -mixing random variables and applications in errors-in-variables regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(3), pages 600-617, September.
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    Cited by:

    1. Zhou, Houlin & Zhu, Hanbing & Wang, Xuejun, 2024. "Change point detection via feedforward neural networks with theoretical guarantees," Computational Statistics & Data Analysis, Elsevier, vol. 193(C).

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