Complete convergence for weighted sums of END random variables and its application to nonparametric regression models

摘要

In this article, the complete convergence for weighted sums of extended negatively dependent (END, for short) random variables is investigated. Some sufficient conditions for the complete convergence are provided. In addition, the Marcinkiewicz-Zygmund type strong law of large numbers for weighted sums of END random variables is obtained. The results obtained in the article generalise and improve the corresponding one of Wang et al. [(2014b), On Complete Convergence for an Extended Negatively Dependent Sequence', Communications in Statistics-Theory and Methods, 43, 2923-2937]. As an application, the complete consistency for the estimator of nonparametric regression model is established.