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Complete convergence for weighted sums of NSD random variables and its application in the EV regression model

Author

Listed:
  • Xuejun Wang
  • Aiting Shen
  • Zhiyong Chen
  • Shuhe Hu

Abstract

In this paper, some basic properties for negatively superadditive-dependent (NSD, in short) random variables are presented, such as the Rosenthal-type inequality and the Kolmogorov-type exponential inequality. Using these properties, we further study the complete convergence for weighted sums of NSD random variables, which generalizes and improves some corresponding ones for independent random variables and negatively associated random variables. Some sufficient conditions to prove the complete convergence for weighted sums of NSD random variables are provided. As an application, the complete consistency of LS estimators in the EV regression model with NSD errors is investigated under mild conditions, which generalizes and improves the corresponding one for negatively associated random variables. Copyright Sociedad de Estadística e Investigación Operativa 2015

Suggested Citation

  • 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.
    • Handle: RePEc:spr:testjl:v:24:y:2015:i:1:p:166-184
    DOI: 10.1007/s11749-014-0402-6
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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. Eghbal, N. & Amini, M. & Bozorgnia, A., 2011. "On the Kolmogorov inequalities for quadratic forms of dependent uniformly bounded random variables," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1112-1120, August.
    3. Christofides, Tasos C. & Vaggelatou, Eutichia, 2004. "A connection between supermodular ordering and positive/negative association," Journal of Multivariate Analysis, Elsevier, vol. 88(1), pages 138-151, January.
    4. Eghbal, N. & Amini, M. & Bozorgnia, A., 2010. "Some maximal inequalities for quadratic forms of negative superadditive dependence random variables," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 587-591, April.
    5. 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.
    6. Wang, Liqun, 1998. "Estimation of censored linear errors-in-variables models," Journal of Econometrics, Elsevier, vol. 84(2), pages 383-400, June.
    7. Guo-Liang Fan & Han-Ying Liang & Jiang-Feng Wang & Hong-Xia Xu, 2010. "Asymptotic properties for LS estimators in EV regression model with dependent errors," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 94(1), pages 89-103, March.
    8. Soo Sung, 2012. "Complete convergence for weighted sums of negatively dependent random variables," Statistical Papers, Springer, vol. 53(1), pages 73-82, February.
    9. Deaton, Angus, 1985. "Panel data from time series of cross-sections," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 109-126.
    10. Hu, Taizhong & Xie, Chaode & Ruan, Lingyan, 2005. "Dependence structures of multivariate Bernoulli random vectors," Journal of Multivariate Analysis, Elsevier, vol. 94(1), pages 172-195, May.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Xuejun Wang & Yi Wu & Shuhe Hu, 2018. "Strong and weak consistency of LS estimators in the EV regression model with negatively superadditive-dependent errors," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(1), pages 41-65, January.
    5. Aiting Shen, 2019. "Asymptotic properties of LS estimators in the errors-in-variables model with MD errors," Statistical Papers, Springer, vol. 60(4), pages 1193-1206, August.

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