Bounds on the constant in the mean central limit theorem
Probability
2010-10-20 v2
Abstract
Let be independent with zero means, finite variances and finite absolute third moments. Let be the distribution function of , where , and that of the standard normal. The -distance between and then satisfies In particular, when are identically distributed with variance , we have \Vert F_n-\Phi\Vert_1\le\frac{E|X_1|^3}{\sigma^3\sqrt{n}}\qquad for all $n\in\mathbb{N}$, corresponding to an -Berry--Esseen constant of 1.
Cite
@article{arxiv.0906.5145,
title = {Bounds on the constant in the mean central limit theorem},
author = {Larry Goldstein},
journal= {arXiv preprint arXiv:0906.5145},
year = {2010}
}
Comments
Published in at http://dx.doi.org/10.1214/10-AOP527 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)