Convergence properties for randomly weighted sums of ρ-mixing sequences with related statistical applications

Abstract

In this paper, we investigate some convergence properties, such as complete convergence, complete moment convergence, complete f-moment convergence and strong law of large numbers, for partial sums of randomly weighted sums of -mixing sequences by using the moment inequality, which extend and improve the corresponding ones in the literature. As applications, we obtain the complete consistency for the randomly weighted estimator in a nonparametric regression models and the estimators for the unknown parameters in the simple linear errors-in-variables regression models based on -mixing errors.