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Complete moment convergence for randomly weighted sums of extended negatively dependent random variables with application to semiparametric regression models

Author

Listed:
  • Nan Cheng

    (Anhui University)

  • Chao Lu

    (Anhui University)

  • Jibing Qi

    (Hefei Normal University)

  • Xuejun Wang

    (Anhui University)

Abstract

In this paper, we investigate the complete moment convergence for randomly weighted sums of extended negatively dependent (END) random variables. The results obtained in this paper extended the corresponding one of Li et al. (J Inequalities Appl 2017:16, 2017). As an application, we study the complete consistency for the estimator of semiparametric regression models based on END random variables by using the complete convergence that we established. Finally, we have conducted comprehensive simulation studies to demonstrate the validity of obtained theoretical results.

Suggested Citation

  • Nan Cheng & Chao Lu & Jibing Qi & Xuejun Wang, 2022. "Complete moment convergence for randomly weighted sums of extended negatively dependent random variables with application to semiparametric regression models," Statistical Papers, Springer, vol. 63(2), pages 397-419, April.
    • Handle: RePEc:spr:stpapr:v:63:y:2022:i:2:d:10.1007_s00362-021-01244-1
    DOI: 10.1007/s00362-021-01244-1
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    References listed on IDEAS

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    1. Xuejun Wang & Yi Wu & Shuhe Hu & Nengxiang Ling, 2020. "Complete moment convergence for negatively orthant dependent random variables and its applications in statistical models," Statistical Papers, Springer, vol. 61(3), pages 1147-1180, June.
    2. Guo, Mingle & Zhu, Dongjin, 2013. "Equivalent conditions of complete moment convergence of weighted sums for ρ∗-mixing sequence of random variables," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 13-20.
    3. Liu, Li, 2009. "Precise large deviations for dependent random variables with heavy tails," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1290-1298, May.
    4. 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.
    5. 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.
    6. Zhou, Xing-cai & Lin, Jin-guan, 2013. "Asymptotic properties of wavelet estimators in semiparametric regression models under dependent errors," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 251-270.
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    Cited by:

    1. Thomas Hitchen & Saralees Nadarajah, 2024. "Exact Results for the Distribution of Randomly Weighted Sums," Mathematics, MDPI, vol. 12(1), pages 1-22, January.

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