Lp convergence and complete convergence for weighted sums of AANA random variables. Issue 22 (17th November 2018)

• Record Type: Journal Article
• Authors: Xi, Mengmei; Deng, Xin; Wang, Xuejun; Cheng, Zhaoyang
• Is Part Of: Communications in statistics. Volume 47:Issue 22(2018)
• Page Start: 5604
• Page End: 5613
• Publication Date: 2018-11-17
• Subjects: AANA sequence -- Weighted sums -- Lp convergence -- Complete convergence.; 60F15 -- 60F25; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2017.1397173
• Languages: English
• ISSNs: 0361-0926

Abstract

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 L p convergence and the complete convergence. As an application, the Marcinkiewicz–Zygmund-type strong law of large numbers for AANA random variables is obtained.