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

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  • Mengmei Xi
  • Xin Deng
  • Xuejun Wang
  • Zhaoyang Cheng

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.

Suggested Citation

  • Mengmei Xi & Xin Deng & Xuejun Wang & Zhaoyang Cheng, 2018. "Lp convergence and complete convergence for weighted sums of AANA random variables," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(22), pages 5604-5613, November.
    • Handle: RePEc:taf:lstaxx:v:47:y:2018:i:22:p:5604-5613
    DOI: 10.1080/03610926.2017.1397173
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    Cited by:

    1. Saisai Ding & Xiaoqin Li & Xiang Dong & Wenzhi Yang, 2020. "The Consistency of the CUSUM-Type Estimator of the Change-Point and Its Application," Mathematics, MDPI, vol. 8(12), pages 1-12, November.

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