An isometric study of the Lindeberg-Feller CLT via Stein's method
Probability
2011-12-30 v1
Abstract
We use Stein's method to prove a generalization of the Lindeberg-Feller CLT providing an upper and a lower bound for the superior limit of the Kolmogorov distance between a normally distributed random variable and the rowwise sums of a rowwise independent triangular array of random variables which is asymptotically negligible in the sense of Feller. A natural example shows that the upper bound is of optimal order. The lower bound improves a result by Andrew Barbour and Peter Hall.
Keywords
Cite
@article{arxiv.1112.5719,
title = {An isometric study of the Lindeberg-Feller CLT via Stein's method},
author = {Ben Berckmoes and Bob Lowen and Jan Van Casteren},
journal= {arXiv preprint arXiv:1112.5719},
year = {2011}
}
Comments
19 pages