Complete moment convergence and complete convergence for weighted sums of NSD random variables

Abstract

In this paper, the equivalent conditions of complete moment convergence of the maximum partial weighted sums for negatively superadditive dependent (NSD) random variables are established without the assumption of identical distribution. As applications, the complete moment convergence, the complete convergence and strong law of large numbers for NSD random variables are obtained. The results obtained in the paper generalize or improve the corresponding ones for weighted sums of independent random variables and negatively associated random variables.

Complete moment convergence for Sung’s type weighted sums of ρ*-mixing random variables

“…The complete convergence and complete moment convergence have attracted many authors. We refer to Bai and Su [2], Baum and Katz [3], Deng et al [12], Li and Spȃtaru [14], Katz [15], Rosalsky et al [17], Wang et al [22], Wang and Hu [23], Wang and Su [25], and their references. Definition 1.2.…”

Complete convergence for weighted sums of pairwise independent random variables

“…Deng et al [14], Zhao et al [15] presented some results on complete convergence for weighted sums of random variables satisfying the Rosenthal type inequality. Xue et al [16], Wang et al [17], Deng et al [18] studied the complete convergence for weighted sums of negatively superadditive-dependent random variables. Qiu and Chen [19] obtained the complete convergence for the weighted sums of widely orthant dependent random variables.…”

On complete moment convergence for weighted sums of negatively superadditive dependent random variables

“…Since the concept of NSD random variables was introduced by Hu [14], many applications for NSD random variables have been established. See, for example, Hu [14] for some basic properties and three structural theorems, Eghbal et al [9] for two maximal inequalities and a strong law of large numbers of quadratic forms of nonnegative NSD random variables, Eghbal et al [10] for some Kolmogorov inequalities for quadratic forms and weighted quadratic forms of nonnegative NSD uniformly bounded random variables, Shen et al [18] for the almost sure convergence and strong stability for weighted sums of NSD random variables, Wang et al [22] for the complete convergence of arrays of rowwise NSD random variables and the complete consistency for the estimator of nonparametric regression model based on NSD errors, Wang et al [23] for the complete convergence for weighted sums of NSD random variables and its application in the EV regression model, Shen et al [20] for some applications of the Rosenthal-type inequality for NSD random variables, Zhang [27] for the strong convergence property of Jamison weighted sums of NSD random variables, Naderi et al [17], Deng et al [8] and Zheng et al [28] for the complete convergence of weighted sums for NSD random variables, Shen et al [19] for the complete moment convergence for arrays of rowwise NSD random variables, Amini et al [2] for the complete convergence of moving average processes based on NSD sequences, among others.…”