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Concentration inequalities for suprema of unbounded empirical processes

Abstract : 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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https://hal.archives-ouvertes.fr/hal-01545101
Contributor : Antoine Marchina Connect in order to contact the contributor
Submitted on : Thursday, March 5, 2020 - 11:57:19 AM
Last modification on : Wednesday, November 3, 2021 - 9:28:56 AM
Long-term archiving on: : Saturday, June 6, 2020 - 2:32:39 PM

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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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