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Pré-Publication, Document De Travail Année : 2020

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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Dates et versions

hal-01545101 , version 1 (22-06-2017)
hal-01545101 , version 2 (05-03-2020)
hal-01545101 , version 3 (09-12-2022)

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  • HAL Id : hal-01545101 , version 2

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Antoine Marchina. Concentration inequalities for suprema of unbounded empirical processes. 2020. ⟨hal-01545101v2⟩
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