Convergence properties for weighted sums of NSD random variables

Aiting Shen, Xinghui Wang and Huayan Zhu

Communications in Statistics - Theory and Methods, 2016, vol. 45, issue 8, 2402-2412

Abstract: Let {Xn, n ⩾ 1} be a sequence of negatively superadditive dependent (NSD, in short) random variables and {bni, 1 ⩽ i ⩽ n, n ⩾ 1} be an array of real numbers. In this article, we study the strong law of large numbers for the weighted sums ∑ni = 1bniXi without identical distribution. We present some sufficient conditions to prove the strong law of large numbers. As an application, the Marcinkiewicz-Zygmund strong law of large numbers for NSD random variables is obtained. In addition, the complete convergence for the weighted sums of NSD random variables is established. Our results generalize and improve some corresponding ones for independent random variables and negatively associated random variables.

Date: 2016
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DOI: 10.1080/03610926.2014.881492

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