Complete convergence and complete moment convergence for weighted sums of random variables satisfying generalized Rosenthal type inequalities and an application

Abstract

This article mainly investigates the complete convergence and complete moment convergence for weighted sums of random variables satisfying generalized Rosenthal type inequalities, which improves the corresponding ones of the literature. As an application, we further research the errors-in-variables (EV, for short) regression models and exhibit the strong consistency for the least square (LS, for short) estimators. In addition, simulation studies are conducted to verify the finite sample performance of theoretical results.