A shorter proof of Kanter's Bessel function concentration bound

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 $I_0(x)+I_1(x)$, 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).

12 pages. Two references added. Accepted for publication by Probability Theory and Related Fields

References in corpus (1)

• Lower bounds for tails of sums of independent symmetric random variables

Cited by in corpus (1)

• Lower bounds for tails of sums of independent symmetric random variables