In this paper, the complete convergence theorems of partial sums and weighted sums for extended negatively dependent random variables in sublinear expectation spaces have been studied and established. Our results extend the corresponding results of classical probability spaces to the case of sublinear expectation spaces.
In this paper, we provide some probability and moment inequalities
(especially the Marcinkiewicz-Zygmund type inequality) for extended
negatively dependent (END, in short) random variables. By using the
Marcinkiewicz-Zygmund type inequality and the truncation method, we
investigate the complete convergence for sums and weighted sums of arrays of
rowwise END random variables. In addition, the complete moment convergence
for END random variables is obtained. Our results generalize and improve the
corresponding ones of Wang et al. [18] and Baek and Park [2].
Abstract
In this paper, the complete convergence for the weighted sums of arrays of rowwise extended negatively dependent (END, for short) random variables is established under some mild conditions. In addition, the Marcinkiewicz-Zygmund type strong law of large numbers for arrays of rowwise END random variables is also obtained. The result obtained in the paper generalizes and improves some corresponding ones for independent random variables and some dependent random variables in some extent. By using the complete convergence that we established, we further study the complete consistency for the weighted estimator in a nonparametric regression model based on END errors.
In this article, we research some conditions for strong law of large numbers (SLLNs) for weighted sums of extended negatively dependent (END) random variables under sublinear expectation space. Our consequences contain the Kolmogorov strong law of large numbers and the Marcinkiewicz strong law of large numbers for weighted sums of extended negatively dependent random variables. Furthermore, our results extend strong law of large numbers for some sequences of random variables from the traditional probability space to the sublinear expectation space context.
Complete Convergence for END Random Variables under Sublinear Expectations
