We show that the $L_1$ norm of the difference between the standard normal distribution and the distribution of the standardized sum of $n$ independent random variables is less than 72 $R_n$, where $R_n$ is a sum of standardized "inside" third and "outside" second moments. We conjecture that 72 can be replaced by 36 or even less. We also prove a similar result for $m$-dependent random variables, but no constant is specified.
Publié le : 1973-06-14
Classification:
$L_p$ Berry-Esseen,
$m$-dependent,
asymptotic normality and error bounds,
60F05,
60F99
@article{1176996944,
author = {Erickson, R. V.},
title = {On an $L\_p$ Version of the Berry-Esseen Theorem for Independent and $m$- Dependent Variables},
journal = {Ann. Probab.},
volume = {1},
number = {5},
year = {1973},
pages = { 497-503},
language = {en},
url = {http://dml.mathdoc.fr/item/1176996944}
}
Erickson, R. V. On an $L_p$ Version of the Berry-Esseen Theorem for Independent and $m$- Dependent Variables. Ann. Probab., Tome 1 (1973) no. 5, pp. 497-503. http://gdmltest.u-ga.fr/item/1176996944/