Concentration around the mean for maxima of empirical processes

Abstract : In this paper we give optimal constants in Talagrand's concentration inequalities for maxima of empirical processes associated to independent and eventually nonidentically distributed random variables. Our approach is based on the entropy method introduced by Ledoux.
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Thierry Klein, Emmanuel Rio. Concentration around the mean for maxima of empirical processes. Annals of Probability, Institute of Mathematical Statistics, 2005, 33 (3), pp.1060-1077. ⟨10.1214/009117905000000044⟩. ⟨hal-01979113⟩

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