On Complete Convergence in Marcinkiewicz-Zygmund Type SLLN for END Random Variables and Its Applications

In this paper, the complete convergence for maximal weighted sums of extended negatively dependent (END, for short) random variables is investigated. Some sufficient conditions for the complete convergence and some applications to a nonparametric model are provided. The results obtained in the paper generalize and improve the corresponding ones of Wang et al. (2014 Wang, X. J., X. Deng, L. L. Zheng, and S. H. Hu. 2014. Complete convergence for arrays of rowwise negatively superadditive-dependent random variables and its applications. A Journal of Theoretical and Applied Statistics 48(4):834–50. Google Scholarb) and Shen, Xue, and Wang (2017 Shen, A., M. Xue, and W. Wang. 2017. Complete convergence for weighted sums of extended negatively dependent random variables. Communications in Statistics – Theory and Methods 46(3):1433–44.Taylor & Francis Online, Web of Science ® , Google Scholar).