The Annals of Statistics

On the Bahadur representation of sample quantiles for dependent sequences

Wei Biao Wu

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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

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

First available in Project Euclid: 5 August 2005

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Zentralblatt MATH identifier

Primary: 62G30: Order statistics; empirical distribution functions 60F05: Central limit and other weak theorems
Secondary: 60F17: Functional limit theorems; invariance principles

Long- and short-range dependence Bahadur representation nonlinear time series almost sure convergence linear process martingale inequalities empirical processes law of the iterated logarithm


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.

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