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Article Dans Une Revue Annales Henri Lebesgue Année : 2021

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 3

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Antoine Marchina. Concentration inequalities for suprema of unbounded empirical processes. Annales Henri Lebesgue, 2021, 4, pp.831-861. ⟨hal-01545101v3⟩
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