The main result of the present paper is a sharp nonuniform bound on the rate of convergence to normality in the central limit theorem for martingales having finite moments of order $2 + 2\delta$ for some $0 < \delta < \infty$. A nonuniform bound on the rate for convergence to mixtures of normal distributions is obtained as a consequence.
Publié le : 1988-10-14
Classification:
Martingale central limit theorem,
rates of convergence,
nonuniform bounds,
mixtures of normal distributions,
60F05,
60G42
@article{1176991592,
author = {Haeusler, Erich and Joos, Konrad},
title = {A Nonuniform Bound on the Rate of Convergence in the Martingale Central Limit Theorem},
journal = {Ann. Probab.},
volume = {16},
number = {4},
year = {1988},
pages = { 1699-1720},
language = {en},
url = {http://dml.mathdoc.fr/item/1176991592}
}
Haeusler, Erich; Joos, Konrad. A Nonuniform Bound on the Rate of Convergence in the Martingale Central Limit Theorem. Ann. Probab., Tome 16 (1988) no. 4, pp. 1699-1720. http://gdmltest.u-ga.fr/item/1176991592/