Complete convergence and complete moment convergence for widely orthant-dependent random variables

Yang Ding, Yi Wu, Songlin Ma, Xinran Tao and Xuejun Wang

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 16, 8278-8294

Abstract: In this paper, we first establish the complete convergence for weighted sums of widely orthant-dependent (WOD, in short) random variables by using the Rosenthal type maximal inequality. Based on the complete convergence, we further study the complete moment convergence for weighted sums of arrays of rowwise WOD random variables which is stochastically dominated by a random variable X. The results obtained in the paper generalize the corresponding ones for some dependent random variables.

Date: 2017
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DOI: 10.1080/03610926.2016.1177085

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