, Volume 27, Issue 2, pp 379–406 | Cite as

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

  • Yi Wu
  • Xuejun WangEmail author
  • Shuhe Hu
  • Lianqiang Yang
Original Paper


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.


Strong law of large numbers Rosenthal-type inequality Double index weight Nonparametric regression model Simple linear errors-in-variables model Strong consistency 

Mathematics Subject Classification

60F15 62G05 62G20 



The authors are most grateful to the Editor-in-Chief, Associate Editor and two anonymous referees for careful reading of the manuscript and valuable suggestions which helped in improving an earlier version of this paper.


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Copyright information

© Sociedad de Estadística e Investigación Operativa 2017

Authors and Affiliations

  1. 1.School of Mathematical ScienceAnhui UniversityHefeiPeople’s Republic of China

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