Lp convergence and complete convergence for weighted sums of AANA random variables

Mengmei Xi, Xin Deng, Xuejun Wang and Zhaoyang Cheng

Communications in Statistics - Theory and Methods, 2018, vol. 47, issue 22, 5604-5613

Abstract: Let {Xn, n ⩾ 1} be a sequence of asymptotically almost negatively associated (AANA, for short) random variables which is stochastically dominated by a random variable X, and {dni, 1 ⩽ i ⩽ n, n ⩾ 1} be a sequence of real function, which is defined on a compact set E. Under some suitable conditions, we investigate some convergence properties for weighted sums of AANA random variables, especially the Lp convergence and the complete convergence. As an application, the Marcinkiewicz–Zygmund-type strong law of large numbers for AANA random variables is obtained.

Date: 2018
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DOI: 10.1080/03610926.2017.1397173

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