## The Annals of Statistics

### On the Bahadur representation of sample quantiles for dependent sequences

Wei Biao Wu

#### Abstract

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.

#### Article information

Source
Ann. Statist., Volume 33, Number 4 (2005), 1934-1963.

Dates
First available in Project Euclid: 5 August 2005

Permanent link to this document
https://projecteuclid.org/euclid.aos/1123250233

Digital Object Identifier
doi:10.1214/009053605000000291

Mathematical Reviews number (MathSciNet)
MR2166566

Zentralblatt MATH identifier
1080.62024

#### Citation

Wu, Wei Biao. On the Bahadur representation of sample quantiles for dependent sequences. Ann. Statist. 33 (2005), no. 4, 1934--1963. doi:10.1214/009053605000000291. https://projecteuclid.org/euclid.aos/1123250233

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