On the Bahadur representation of sample quantiles for dependent sequences

• 成果类型: Article
• 署名作者: Wu, WB
• 署名单位: University of Chicago
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053605000000291
• 发表日期: 2005
• 页码: 1934-1963
• 关键词: iterated random functions; central-limit-theorem; stationary-processes; Empirical Process; linear-processes; moment inequalities; INFINITE-VARIANCE; Moving averages; U-statistics; strong laws

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.