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 -> infinity, 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 important data often are heavy-tailed and quantile based methods play an role in various problems in finance, including hedging and risk management.
Lahiri, S. N.,
& Sun, S.
(2009). A Berry-Esseen Theorem for Sample Quantiles Under Weak Dependence. Annals of Applied Probability, 19 (1), 108-126.