Strong Limit Theorems for Weighted Sums of Negatively Associated Random Variables

Bing-Yi Jing () and Han-Ying Liang ()
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Bing-Yi Jing: Hong Kong Univ. of Science and Technology
Han-Ying Liang: Tongji University

Journal of Theoretical Probability, 2008, vol. 21, issue 4, 890-909

Abstract: Abstract In this paper, we establish strong laws for weighted sums of identically distributed negatively associated random variables. Marcinkiewicz-Zygmund’s strong law of large numbers is extended to weighted sums of negatively associated random variables. Furthermore, we investigate various limit properties of Cesàro’s and Riesz’s sums of negatively associated random variables. Some of the results in the i.i.d. setting, such as those in Jajte (Ann. Probab. 31(1), 409–412, 2003), Bai and Cheng (Stat. Probab. Lett. 46, 105–112, 2000), Li et al. (J. Theor. Probab. 8, 49–76, 1995) and Gut (Probab. Theory Relat. Fields 97, 169–178, 1993) are also improved and extended to the negatively associated setting.

Keywords: Strong law; Weighted sum; Cesàro mean; Complete convergence; Negatively associated random variable; 60F15 (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1007/s10959-007-0128-4

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