A shorter proof of Kanter's Bessel function concentration bound
Probability
2007-05-23 v2 Classical Analysis and ODEs
Abstract
We give a shorter proof of Kanter's (1976) sharp Bessel function bound for concentrations of sums of independent symmetric random vectors. We provide sharp upper bounds for the sum of modified Bessel functions , which might be of independent interest. Corollaries improve concentration or smoothness bounds for sums of independent random variables due to Cekanavicius & Roos (2006), Roos (2005), Barbour & Xia 1999), and Le Cam (1986).
Keywords
Cite
@article{arxiv.math/0603522,
title = {A shorter proof of Kanter's Bessel function concentration bound},
author = {Lutz Mattner and Bero Roos},
journal= {arXiv preprint arXiv:math/0603522},
year = {2007}
}
Comments
12 pages. Two references added. Accepted for publication by Probability Theory and Related Fields