We prove Berry--Esseen bounds for a general class of asymptotically normal statistics which are functions of [math] weakly dependent random variables under easily verifiable conditions. In particular, we show, for some [math] , the validity of the bound [math] for [math] -statistics, studentized means, functions of sample means, functionals of empirical distribution functions and linear combinations of order statistics.
Publié le : 1997-09-14
Classification:
absolute regularity,
asymptotically normal statistics,
Berry-Esseen bounds,
functionals of empirical distribution functions,
functions of sample means,
linear combinations of order statistics,
mixing,
studentized means,
U-statistics,
weakly dependent random variables
@article{1177334459,
author = {Bentkus, V. and G\"otze, F. and Tikhomoirov, A.},
title = {Berry-Esseen bounds for statistics of weakly dependent samples},
journal = {Bernoulli},
volume = {3},
number = {3},
year = {1997},
pages = { 329-349},
language = {en},
url = {http://dml.mathdoc.fr/item/1177334459}
}
Bentkus, V.; Götze, F.; Tikhomoirov, A. Berry-Esseen bounds for statistics of weakly dependent samples. Bernoulli, Tome 3 (1997) no. 3, pp. 329-349. http://gdmltest.u-ga.fr/item/1177334459/