Lr convergence for arrays of rowwise asymptotically almost negatively associated random variables

Aiting Shen and Deping Shi

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 23, 11801-11812

Abstract: Let {Xnk, k ⩾ 1, n ⩾ 1} be an array of rowwise asymptotically almost negatively associated random variables and {an, n ⩾ 1} be a sequence of positive real numbers such that an↑∞. Under some suitable conditions, Lr convergence of 1anmax1≤j≤n|∑k=1jXnk|$\frac{1}{a_n} \mathop{\max }\nolimits_{1\le j\le n}^{}|\sum _{k=1}^j X_{nk}|$ is studied. The results obtained in the paper generalize and improve some corresponding ones for negatively associated random variables and independent random variables.

Date: 2017
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DOI: 10.1080/03610926.2017.1285932

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