Complete convergence of weighted sums under negative dependence

Abstract

Negatively dependent, Complete convergence, Weighted sums, 60F15,

Moment inequalities for m-negatively associated random variables and their applications

“…As pointed out and proved by Joag-Dev and Proschan (1983), a number of well-known multivariate distributions possess the NA property, such as multinomial, convolution of unlike multionmial, multivariate hypergeometric, Dirichlet, permutation distribution, negatively correlated normal distribution, random sampling without replacement and joint distribution of ranks. For more details about NA random variables, one can refer to Matula (1992), Shao (2000), Chen et al (2008), Ling (2008), Liang and Zhang (2010), Sung (2011), Zarei and Jabbari (2011), Hu (2012, 2014), Wang et al (2011Wang et al ( , 2014a, and so on.…”

On the Complete Convergence for Arrays of Rowwise Extended Negatively Dependent Random Variables

“…random variables converges completely to the expected value if the variance of the summands is finite. This result has been generalized and extended in several directions, see Gut ([3], [4]), Hu et al ( [7], [8]), Chen et al ( [2]), Sung ([14], [15], [17]), Zarei and Jabbari ( [20]), Baek et al ([1]). In particular, Sung ([14]) obtained the following two Theorems A and B.…”

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.…”