Some strong limit theorems for arrays of rowwise negatively orthant-dependent random variables

Abstract

In this article, the strong limit theorems for arrays of rowwise negatively orthantdependent random variables are studied. Some sufficient conditions for strong law of large numbers for an array of rowwise negatively orthant-dependent random variables without assumptions of identical distribution and stochastic domination are presented. As an application, the Chung-type strong law of large numbers for arrays of rowwise negatively orthant-dependent random variables is obtained. MR(2000) Subject Classification: 60F15

Equivalent Conditions of Complete Moment Convergence and Complete Integral Convergence for Nod Sequences

“…A number of useful results for NOD random variables have been established by many authors. We refer to Volodin [19] for the Kolmogorov exponential inequality, Asadian et al [1] for Rosenthal's type inequality, Zarei and Jabbari [28], Wu [24], Wang et al [20], Sung [18], Yi et al [27] and Chen and Sung [4] for complete convergence, Wang et al [21] and Sung [17] for exponential inequalities, Wu and Jiang [25] for the strong consistency of M estimator in a linear model, Shen [12,14] for strong limit theorems of weighted sums, Shen [15] for the asymptotic approximation of inverse moments, Wang and Si [22] for the complete consistency of estimator of nonparametric regression model, Qiu et al [11] and Wu and Volodin [26] for the complete moment convergence, and so on.…”

Complete Moment Convergence for Arrays of Rowwiseφ-Mixing Random Variables

“…For more details about this type of complete convergence, one can refer to Gan and Chen [3], Wu et al [15], Wu [16], Huang et al [17], Shen [18], Shen et al [19,20], and so on. The purpose of this paper is extending Theorem A to the complete moment convergence, which is a more general version of the complete convergence, and making some improvements such that the conditions are more general.…”

Exponential probability inequalities for WNOD random variables and their applications

“…If both (1.1) and (1.2) hold for g L (n) = g U (n) = 1 for any n ≥ 1, then the random variables {X n , n ≥ 1} are called negatively orthant dependent (NOD, in short). For more details about NOD sequence, one can refer to Fakoor and Azarnoosh [6], Asadian et al [1], Wang et al [26,27], Wu [37,38], Wu and Jiang [39], Sung [21], Nili Sani et al [11], Li et al [8], Shen [16,18,20], and so on. It is well known that NA random variables are NOD random variables.…”