Concentration inequalities for suprema of unbounded empirical processes
Résumé
In this paper, we provide new concentration inequalities for suprema of (possibly) non-centered and unbounded empirical processes associated with independent and identically distributed random variables. In particular, we establish Fuk-Nagaev type inequalities with the optimal constant in the moderate deviation bandwidth. The proof builds on martingale methods and comparison inequalities, allowing to bound generalized quantiles as the so-called Conditional Value-at-Risk. Importantly, we also extent the left concentration inequalities of Klein (2002) to classes of unbounded functions.
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