In this paper, we give estimates of the minimal ${\mathbb{L}}^{1}$ distance between the distribution of the normalized partial sum and the limiting Gaussian distribution for stationary sequences satisfying projective criteria in the style of Gordin or weak dependence conditions.
Publié le : 2008-08-15
Classification:
Mean central limit theorem,
Wasserstein distance,
Minimal distance,
Martingale difference sequences,
Strong mixing,
Stationary sequences,
Weak dependence,
Rates of convergence,
Projective criteria,
60F05
@article{1217964116,
author = {Dedecker, J\'er\^ome and Rio, Emmanuel},
title = {On mean central limit theorems for stationary sequences},
journal = {Ann. Inst. H. Poincar\'e Probab. Statist.},
volume = {44},
number = {2},
year = {2008},
pages = { 693-726},
language = {en},
url = {http://dml.mathdoc.fr/item/1217964116}
}
Dedecker, Jérôme; Rio, Emmanuel. On mean central limit theorems for stationary sequences. Ann. Inst. H. Poincaré Probab. Statist., Tome 44 (2008) no. 2, pp. 693-726. http://gdmltest.u-ga.fr/item/1217964116/