On the Rate of Complete Convergence for Weighted Sums of Arrays of Rowwise ϕ-Mixing Random Variables

Aiting Shen, Xinghui Wang, Xiaoqin Li and Xuejun Wang

Communications in Statistics - Theory and Methods, 2014, vol. 43, issue 13, 2714-2725

Abstract: Let {Xni,i≥1,n≥1}$\lbrace X_{\scriptsize\textit{ni}}, i\ge 1, n\ge 1\rbrace$ be an array of rowwise ϕ-mixing random variables. A rate of complete convergence for weighted sums of arrays of rowwise ϕ-mixing random variables is obtained without assumption of identical distribution. The techniques used in the paper are the Rosenthal type inequality and the truncated method. As an application, the Baum and Katz type result for arrays of rowwise ϕ-mixing random variables is obtained.

Date: 2014
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DOI: 10.1080/03610926.2012.683130

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