Open Access
January 2008 Local tail bounds for functions of independent random variables
Luc Devroye, Gábor Lugosi
Ann. Probab. 36(1): 143-159 (January 2008). DOI: 10.1214/00911797000000088


It is shown that functions defined on {0, 1, …, r−1}n satisfying certain conditions of bounded differences that guarantee sub-Gaussian tail behavior also satisfy a much stronger “local” sub-Gaussian property. For self-bounding and configuration functions we derive analogous locally subexponential behavior. The key tool is Talagrand’s [Ann. Probab. 22 (1994) 1576–1587] variance inequality for functions defined on the binary hypercube which we extend to functions of uniformly distributed random variables defined on {0, 1, …, r−1}n for r≥2.


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Luc Devroye. Gábor Lugosi. "Local tail bounds for functions of independent random variables." Ann. Probab. 36 (1) 143 - 159, January 2008.


Published: January 2008
First available in Project Euclid: 28 November 2007

zbMATH: 1130.60033
MathSciNet: MR2370601
Digital Object Identifier: 10.1214/00911797000000088

Primary: 60F10

Keywords: Concentration inequalities , configuration functions , convex distance , hypercontractivity , Talagrand’s inequality

Rights: Copyright © 2008 Institute of Mathematical Statistics

Vol.36 • No. 1 • January 2008
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