Some strong convergence properties for randomly weighted maximum partial sums of END random variables with statistical applications

Abstract

This article mainly studies the strong convergence properties for randomly weighted maximum partial sums of arrays of row-wise extended negatively dependent (END, for short) random variables, including the complete moment convergence and complete f-moment convergence. The results obtained in this paper extend the corresponding ones in the literature. As an application, we investigate the complete consistency of the estimators of nonparametric regression models based on END random errors by using the complete convergence that we established. Then we provide comprehensive simulation studies to demonstrate the validity of the theoretical results based on the finite sample performance. Finally, an application to a real data set is illustrated.