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Strong Convergence for Weighted Sums of Widely Orthant Dependent Random Variables and Applications

Author

Listed:
  • Yi Wu

    (Anhui University
    Chizhou University)

  • Xuejun Wang

    (Anhui University)

  • Aiting Shen

    (Anhui University)

Abstract

In this paper, the complete convergence and the Kolmogorov strong law of large numbers for weighted sums of widely orthant dependent random variables are presented. Some applications to simple linear errors-in-variables model, nonparametric regression model, and quasi-renewal counting process are provided. Simulation studies are also carried out to confirm the theoretical results.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:25:y:2023:i:1:d:10.1007_s11009-023-09976-3
    DOI: 10.1007/s11009-023-09976-3
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    References listed on IDEAS

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    1. Fan, Y., 1990. "Consistent nonparametric multiple regression for dependent heterogeneous processes: The fixed design case," Journal of Multivariate Analysis, Elsevier, vol. 33(1), pages 72-88, April.
    2. Thanh, Le Van & Yin, G., 2015. "Weighted sums of strongly mixing random variables with an application to nonparametric regression," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 195-202.
    3. 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.
    4. 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.
    5. Roussas, George G. & Tran, Lanh T. & Ioannides, D. A., 1992. "Fixed design regression for time series: Asymptotic normality," Journal of Multivariate Analysis, Elsevier, vol. 40(2), pages 262-291, February.
    6. Liu, Li, 2009. "Precise large deviations for dependent random variables with heavy tails," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1290-1298, May.
    7. Bai, Z. D. & Cheng, Philip E., 2000. "Marcinkiewicz strong laws for linear statistics," Statistics & Probability Letters, Elsevier, vol. 46(2), pages 105-112, January.
    8. Deaton, Angus, 1985. "Panel data from time series of cross-sections," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 109-126.
    9. 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.
    10. 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.
    11. Aiting Shen, 2013. "Bernstein-Type Inequality for Widely Dependent Sequence and Its Application to Nonparametric Regression Models," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, July.
    12. Xuejun Wang & Chen Xu & Tien-Chung Hu & Andrei Volodin & Shuhe Hu, 2014. "On complete convergence for widely orthant-dependent random variables and its applications in nonparametric regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 607-629, September.
    13. Roussas, George G., 1989. "Consistent regression estimation with fixed design points under dependence conditions," Statistics & Probability Letters, Elsevier, vol. 8(1), pages 41-50, May.
    14. Liang, Han-Ying & Jing, Bing-Yi, 2005. "Asymptotic properties for estimates of nonparametric regression models based on negatively associated sequences," Journal of Multivariate Analysis, Elsevier, vol. 95(2), pages 227-245, August.
    15. 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.
    16. Kaiyong Wang & Yuebao Wang & Qingwu Gao, 2013. "Uniform Asymptotics for the Finite-Time Ruin Probability of a Dependent Risk Model with a Constant Interest Rate," Methodology and Computing in Applied Probability, Springer, vol. 15(1), pages 109-124, March.
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