We give uniform rates of convergence in the central limit theorem for associated processes with finite third moment. No stationarity is required. Using a coefficient $u(n)$ which describes the covariance structure of the process, we obtain a convergence rate $O(n^{-1/2}\log^2n)$ if $u(n)$ exponentially decreases to 0. An example shows that such a rate can no longer be obtained if $u(n)$ decreases only as a power.
Publié le : 1988-10-14
Classification:
Central limit theorem,
associated random variables,
convergence rate,
60F05,
62H20
@article{1176991591,
author = {Birkel, Thomas},
title = {On the Convergence Rate in the Central Limit Theorem for Associated Processes},
journal = {Ann. Probab.},
volume = {16},
number = {4},
year = {1988},
pages = { 1685-1698},
language = {en},
url = {http://dml.mathdoc.fr/item/1176991591}
}
Birkel, Thomas. On the Convergence Rate in the Central Limit Theorem for Associated Processes. Ann. Probab., Tome 16 (1988) no. 4, pp. 1685-1698. http://gdmltest.u-ga.fr/item/1176991591/