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

被引：0

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.

引用

页码：145 / 156

页数：12

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

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