A Note on Talagrand's Concentration Inequality
Dmitriy Panchenko, University of New Mexico
Abstract
In this paper we revisit Talagrand's proof of
concentration inequality for empirical processes. We give a different proof
of the main technical lemma
that guarantees the existence of a certain kernel. Moreover, we generalize
the result of Talagrand to a family of kernels which in one particular
case allows us to produce the Poissonian bound without using the truncation
argument. We also give some examples of applications of the abstract concentration
inequality to empirical processes that demonstrate some interesting properties
of Talagrand's kernel method.
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