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Local tail bounds for functions of independent random variables
Luc Devroye and Gábor Lugosi
Annals of Probability
Volume to appear,
,
2006.
AbstractIt is shown that functions defined on $\{0,1,\ldots,r-1\}^n$
satisfying certain conditions of bounded differences that
guarantee subgaussian tail behavior also satisfy a much
stronger ``local'' subgaussian property. For self-bounding
and configuration functions we derive analogous locally
subexponential behavior.
The key tool is Talagrand's (1994) variance inequality
for functions defined on the binary hypercube
which we extend to functions of uniformly distributed
random variables defined on $\{0,1,\ldots,r-1\}^n$ for $r\ge 2$. [Edit]
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