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

摘要

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.