On the Bahadur representation of sample quantiles for dependent sequences

被引：82
|
作者：
Wu, WB [1 ]
机构：
[1] Univ Chicago, Dept Stat, Chicago, IL 60637 USA
来源：
ANNALS OF STATISTICS | 2005年 / 33卷 / 04期
关键词：
long- and short-range dependence; Bahadur representation; nonlinear time series; almost sure convergence; linear process; martingale inequalities; empirical processes; law of iterated logarithm;
D O I：
10.1214/009053605000000291
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：
We establish the Bahadur representation of sample quantiles for linear and some widely used nonlinear processes. Local fluctuations of empirical processes are discussed. Applications to the trimmed and Winsorized means are given. Our results extend previous ones by establishing sharper bounds under milder conditions and thus provide new insight into the theory of empirical processes for dependent random variables.
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页码：1934 / 1963
页数：30
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