On Bahadur representation for sample quantiles under α-mixing sequence

被引：19
|
作者：
Zhang, Qinchi [1 ]
Yang, Wenzhi [2 ]
Hu, Shuhe [2 ]
机构：
[1] Univ Sci & Technol China, Dept Stat & Finance, Hefei 230026, Peoples R China
[2] Anhui Univ, Sch Math Sci, Hefei 230039, Peoples R China
来源：
STATISTICAL PAPERS | 2014年 / 55卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Bahadur representation; Sample quantile; alpha-Mixing sequence; Convergence rate;
D O I：
10.1007/s00362-012-0472-z
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, by relaxing the mixing coefficients to alpha(n) = O(n (-beta)), beta > 3, we investigate the Bahadur representation of sample quantiles under alpha-mixing sequence and obtain the rate as O (n(- /12) (long long n center dot log n)(1/2) ). Meanwhile, for any delta > 0, by strengthening the mixing coefficients to alpha(n) = O(n (-I2) ), beta > mas {3 + 5/1+delta, 1+ 2/delta} , we have the rate as O(n -3/4+delta/4(2+delta) (log log n center dot log n)(1/2)Specifically, if delta = root 41-5/4 and beta > root 41+7/2, then the rate is presented as Omicron ( n (-root 41+5/ 16) (log log n center dot log n)(1/2).)
引用
收藏
页码：285 / 299
页数：15
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