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 suc-
cessively 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.

EB00000004456K

Available

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