Complete convergence for arrays of rowwise m n -extended negatively dependent random variables and its application

Abstract

. In this article, under some proper and sufficient conditions, we gave complete convergence for weighted sums and maximal weighted sums of arrays of rowwise m n -extended negatively dependent (rowwise m n -END) random variables, which is a new dependent structure. In addition, a relationship between { m n , n ≥ 1 } and moment condition for convergence is revealed in a sense. The results obtained in the article generalize some corresponding ones for independent and some dependent random variables. As an application, the strong consistency for the weighted estimator in a non parametric regression model is established.