Complete $f$-moment convergence for randomly weighted sums of extended negatively dependent random variables and its statistical application

In this paper, we investigate the complete $f$-moment convergence for randomly weighted sums of extended negatively dependent (END for short) random variables. Some results obtained in this paper extend and improve the corresponding ones of P. Li, X. Li, and K. Wu [J. Inequal. Appl., 2017 (2017), 182]. As an application of our main results, we establish the strong consistency for the least square (LS for short) estimators in the simple linear errors-in-variables (EV for short) regression models and provide a simulation study to verify our theoretical results.