Complete convergence for weighted sums of random variables satisfying generalized Rosenthal-type inequalities*

Abstract

In the paper, we establish the complete convergence for weighted sums of random variables satisfying generalized Rosenthal-type inequalities. Our results partially extend some known results and weaken their conditions. As statistical applications, we study the nonparametric regression model and obtain the complete consistency of the weighted regression estimator for the unknown regression functions.