Normal Approximation for Weighted Sums under a Second Order Correlation Condition
Probability
2019-06-24 v1
Abstract
Under correlation-type conditions, we derive an upper bound of order for the average Kolmogorov distance between the distributions of weighted sums of dependent summands and the normal law. The result is based on improved concentration inequalities on high-dimensional Euclidean spheres. Applications are illustrated on the example of log-concave probability measures.
Cite
@article{arxiv.1906.09063,
title = {Normal Approximation for Weighted Sums under a Second Order Correlation Condition},
author = {S. G. Bobkov and G. P. Chistyakov and F. Götze},
journal= {arXiv preprint arXiv:1906.09063},
year = {2019}
}