A shorter proof of Kanter's Bessel function concentration bound

• 成果类型: Article
• 署名作者: Mattner, Lutz; Roos, Bero
• 署名单位: University of Lubeck; University of Hamburg
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-006-0043-0
• 发表日期: 2007
• 页码: 191-205
• 关键词: INEQUALITIES; successes; number

摘要

We give a shorter proof of Kanter's (J. Multivariate Anal. 6, 222-236, 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 (Lith. Math. J. 46, 54-91, 2006); Roos (Bernoulli, 11, 533-557, 2005), Barbour & Xia (ESAIM Probab. Stat. 3, 131-150, 1999), and Le Cam (Asymptotic Methods in Statistical Decision Theory. Springer, Berlin Heidelberg New York, 1986).