Some improved results on Berry-Esseen bounds for strong mixing random variables and applications

被引：1

作者：

Wu, Yi ^{[1
]}

Hu, Tien-Chung ^{[2
]}

Volodin, Andrei ^{[3
,4
,5
]}

Wang, Xuejun ^{[6
]}

机构：

[1] Chizhou Univ, Sch Big Data & Artificial Intelligence, Chizhou, Peoples R China

[2] Natl Tsing Hua Univ, Dept Math, Hsinchu, Taiwan

[3] Xiamen Univ Technol, Sino Canada Res Ctr Nonlinear Dynam & Noise Contro, Xiamen, Fujian, Peoples R China

[4] Univ Regina, Xiamen Univ Technol, Xiamen, Fujian, Peoples R China

[5] Univ Regina, Dept Mathematicsand Stat, Regina, SK, Canada

[6] Anhui Univ, Sch Big Data & Stat, Hefei 230601, Peoples R China

来源：

STATISTICS | 2023年 / 57卷 / 03期

关键词：

Berry-Esseen bound; alpha-mixing random variables; sample quantiles; central limit theorem; SAMPLE QUANTILES; BAHADUR REPRESENTATION; SEQUENCES; THEOREM;

D O I：

10.1080/02331888.2023.2213460

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：

In this paper, we mainly establish a general form of Berry-Esseen bound for a-mixing random variables. With different choices of the parameters, the rates are shown as O(n(-3/26)), O(n(-1/6)), and approximately O(n(-1/4)). These results improved some corresponding ones in the literature. An application to the Berry-Esseen bound of sample quantiles is further provided. Moreover, some simulations are also carried out to support the theoretical results.

引用

页码：740 / 760

页数：21

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