The Annals of Applied Probability

A Berry–Esseen theorem for sample quantiles under weak dependence

S. N. Lahiri and S. Sun

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This paper proves a Berry–Esseen theorem for sample quantiles of strongly-mixing random variables under a polynomial mixing rate. The rate of normal approximation is shown to be O(n−1/2) as n→∞, where n denotes the sample size. This result is in sharp contrast to the case of the sample mean of strongly-mixing random variables where the rate O(n−1/2) is not known even under an exponential strong mixing rate. The main result of the paper has applications in finance and econometrics as financial time series data often are heavy-tailed and quantile based methods play an important role in various problems in finance, including hedging and risk management.

Article information

Ann. Appl. Probab., Volume 19, Number 1 (2009), 108-126.

First available in Project Euclid: 20 February 2009

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Zentralblatt MATH identifier

Primary: 60F05: Central limit and other weak theorems
Secondary: 60G10: Stationary processes 62E20: Asymptotic distribution theory

Normal approximation quantile hedging stationary strong mixing


Lahiri, S. N.; Sun, S. A Berry–Esseen theorem for sample quantiles under weak dependence. Ann. Appl. Probab. 19 (2009), no. 1, 108--126. doi:10.1214/08-AAP533.

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