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ON THE COMPLETE CONVERGENCE OF WEIGHTED SUMS FOR DEPENDENT RANDOM VARIABLES  

BAEK JONG-IL (School of Mathematical Science and Institute of Basic Natural Science, Wonkwang University)
PARK SUNG-TAE (Division of Business Administration, Wonkwang University)
CHUNG SUNG-Mo (School of Mathematical Science and Institute of Basic Natural Science, Wonkwang University)
LIANG HAN-YING (Department of Applied Mathematics, Tongji University)
LEE CHUNG YEL (School of Mathematical Science and Institute of Basic Natural Science, Wonkwang University)
Publication Information
Journal of the Korean Statistical Society / v.34, no.1, 2005 , pp. 21-33 More about this Journal
Abstract
Let ｛X/sun ni/ ｜ 1 ≤ i ≤ n, n ≥ 1 ｝ be an array of rowwise negatively associated random variables. We in this paper discuss the conditions of n/sup -1/p/ (equation omitted) →0 completely as n → ∞ for some 1 ≤ p < 2 under not necessarily identically distributed setting. As application, it is obtained that n/sup -1/p/ (equation omitted) →0 completely as n → ∞ if and only if E｜X/sub 11/｜/sup 2p/ < ∞ and EX/sub ni=0 under identically distributed case such that the corresponding results on i. i. d. case are extended and the strong convergence for weighted sums of rowwise negatively associated arrays is also considered.
Keywords
Negatively associated random variables; array; strong convergence; complete convergence;
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