Local tail bounds for functions of independent random variables
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The Annals of Probability

Local tail bounds for functions of independent random variables

Luc Devroye and Gábor Lugosi

Source: Ann. Probab. Volume 36, Number 1 (2008), 143-159.

Abstract

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.

Primary Subjects: 60F10
Keywords: Concentration inequalities; convex distance; configuration functions; hypercontractivity; Talagrand’s inequality

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Permanent link to this document: http://projecteuclid.org/euclid.aop/1196268676
Digital Object Identifier: doi:10.1214/00911797000000088

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