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Weighted version of strong law of large numbers for a class of random variables and its applications

Author

Listed:
  • Yi Wu

    (Anhui University)

  • Xuejun Wang

    (Anhui University)

  • Shuhe Hu

    (Anhui University)

  • Lianqiang Yang

    (Anhui University)

Abstract

In this paper, the single index weighted version of Marcinkiewicz–Zygmund type strong law of large numbers and the double index weighted version of Marcinkiewicz–Zygmund type strong law of large numbers are investigated successively for a class of random variables, which extends the classical results for independent and identically distributed random variables. As applications of the results, we further study the strong consistency for the weighted estimator in the nonparametric regression model and the least square estimators in the simple linear errors-in-variables model. Moreover, we also present some numerical study to verify the validity of our results.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:testjl:v:27:y:2018:i:2:d:10.1007_s11749-017-0550-6
    DOI: 10.1007/s11749-017-0550-6
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    References listed on IDEAS

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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.

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