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Strong laws for weighted sums of $$\psi $$ ψ -mixing random variables and applications in errors-in-variables regression models

Author

Listed:
  • Di Hu

    (Jinan University)

  • Pingyan Chen

    (Jinan University)

  • Soo Hak Sung

    (Pai Chai University)

Abstract

In this paper, we establish strong laws for weighted sums of identically distributed $$\psi $$ ψ -mixing random variables without any conditions on mixing rate. The classical Kolmogorov strong law of large numbers is extended to weighted sums of $$\psi $$ ψ -mixing random variables. Two types of weights are considered for the weighted sums. These results are applied to the least-squares estimators in the simple linear errors-in-variables regression model when the errors are $$\psi $$ ψ -mixing random vectors.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:testjl:v:26:y:2017:i:3:d:10.1007_s11749-017-0526-6
    DOI: 10.1007/s11749-017-0526-6
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    References listed on IDEAS

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    1. 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.
    2. Bai, Z. D. & Cheng, Philip E., 2000. "Marcinkiewicz strong laws for linear statistics," Statistics & Probability Letters, Elsevier, vol. 46(2), pages 105-112, January.
    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. 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.
    5. Deaton, Angus, 1985. "Panel data from time series of cross-sections," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 109-126.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.

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