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Article
A Berry-Esseen Theorem for Sample Quantiles Under Weak Dependence
Annals of Applied Probability
Document Type
Article
Publication Date
2-1-2009
Disciplines
Abstract
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.
DOI
10.1214/08-AAP533
Citation Information
S. N Lahiri and Shuxia Sun. "A Berry-Esseen Theorem for Sample Quantiles Under Weak Dependence" Annals of Applied Probability Vol. 19 Iss. 1 (2009) p. 108 - 126 ISSN: 1050-5164 Available at: http://works.bepress.com/shuxia_sun/1/
Original publication is available at http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.aoap/1235140334