Strong convergence properties for weighted sums of WNOD random variables and its applications in nonparametric regression models

In this article, the complete convergence for the maximum of weighted sums of widely negative orthant dependent (WNOD, in short) random variables is investigated under some suitable moment conditions. Some sufficient conditions to prove the complete convergence are provided. The results obtained in the paper generalize some corresponding ones for some dependent random variables. As an application, the complete consistency for the weighted estimator in a nonparametric regression model is established. Finally, we present some simulations to show the consistency for the nearest neighbour weight function estimator in a nonparametric regression model.