On the error bound in the normal approximation for Jack measures
Probability
2020-06-16 v3
Abstract
In this paper, we obtain uniform and non-uniform bounds on the Kolmogorov distance in the normal approximation for Jack deformations of the character ratio, by using Stein's method and zero-bias couplings. Our uniform bound comes very close to that conjectured by Fulman [J. Combin. Theory Ser. A, 108 (2004), 275--296]. As a by-product of the proof of the non-uniform bound, we obtain a Rosenthal-type inequality for zero-bias couplings.
Keywords
Cite
@article{arxiv.1902.03476,
title = {On the error bound in the normal approximation for Jack measures},
author = {Louis H. Y. Chen and Martin Raič and Lê Văn Thành},
journal= {arXiv preprint arXiv:1902.03476},
year = {2020}
}