Asymptotic Expansions and two-sided Bounds in Randomized Central Limit Theorems
Probability
2023-08-08 v1
Abstract
Lower and upper bounds are explored for the uniform (Kolmogorov) and -distances between the distributions of weighted sums of dependent summands and the normal law. The results are illustrated for several classes of random variables whose joint distributions are supported on Euclidean spheres. We also survey several results on improved rates of normal approximation in randomized central limit theorems.
Cite
@article{arxiv.2308.02693,
title = {Asymptotic Expansions and two-sided Bounds in Randomized Central Limit Theorems},
author = {S. G. Bobkov and G. P. Chistyakov and F. Götze},
journal= {arXiv preprint arXiv:2308.02693},
year = {2023}
}