Complete q-th moment convergence and its statistical applications

Abstract

In this paper, we mainly investigate the complete q-th moment convergence for sums of widely orthant dependent random variables by utilizing the Rosenthal type moment inequality and truncation method. Some sufficient conditions for the complete q-th moment convergence are provided. The results obtained in the paper generalize some corresponding ones of negatively associated random variables in the literature. As an application, the complete consistency for the weighted estimator in a nonparametric regression model is established, and the simulation studies are presented to show the consistency for the nearest neighbor weight function estimator in a nonparametric regression model.