A BOUND IN THE STABLE (α), 1 < α ≤ 2, LIMIT THEOREM FOR ASSOCIATED RANDOM VARIABLES WITH INFINITE VARIANCE

被引：0
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作者：
Sreehari, M. [1 ,2 ]
机构：
[1] Maharaja Sayajirao Univ Baroda, Fac Sci, Dept Stat, Vadodara 390002, India
[2] 6-B Trupti,Vrundavan Pk,New Sama Rd,Chani Rd PO, Vadodara 390024, India
来源：
THEORY OF PROBABILITY AND MATHEMATICAL STATISTICS | 2021年 / 104卷
关键词：
Associated random variables; central limit theorem; stable limit theorem; rate of convergence; non-normal attraction; Berry-Esseen type bound; CONVERGENCE RATE; SEQUENCES;
D O I：
10.1090/tpms/1151
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
Consider a stationary sequence {X-n} of associated random variables with the common distribution function F which is in the domain of non-normal attraction of the normal law or in the domain of attraction of a symmetric stable (alpha) law for alpha < 2. Louhichi and Soulier [13] proved the central limit theorem when F has infinite variance and also proved the stable limit theorem for {X-n} when F is in the domain of normal attraction of the stable law. The aim of this article is to obtain bounds for the rate of convergence in the stable (alpha) limit theorem for 1 < alpha <= 2 when F is in the domain of non-normal attraction. We consider also the rate of convergence problem when F is in the domain of normal attraction of a stable (alpha) law for 1 < alpha < 2.
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页码：145 / 156
页数：12
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