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.
Publié le : 2009-02-15
Classification:
Normal approximation,
quantile hedging,
stationary,
strong mixing,
60F05,
60G10,
62E20
@article{1235140334,
author = {Lahiri, S. N. and Sun, S.},
title = {A Berry--Esseen theorem for sample quantiles under weak dependence},
journal = {Ann. Appl. Probab.},
volume = {19},
number = {1},
year = {2009},
pages = { 108-126},
language = {en},
url = {http://dml.mathdoc.fr/item/1235140334}
}
Lahiri, S. N.; Sun, S. A Berry–Esseen theorem for sample quantiles under weak dependence. Ann. Appl. Probab., Tome 19 (2009) no. 1, pp. 108-126. http://gdmltest.u-ga.fr/item/1235140334/