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Orlicz norms and concentration inequalities for β-heavy tailed random variables

Abstract : We establish a new concentration-of-measure inequality for the sum of independent random variables with β-heavy tail. This includes exponential of Gaussian distributions (a.k.a. log-normal distributions), or exponential of Weibull distributions, among others. These distributions have finite polyno- mial moments at any order but may not have finite α-exponential moments. We exhibit a Orlicz norm adapted to this setting of β-heavy tails, we prove a new Talagrand inequality for the sum and a new maximal inequality. As consequence, a bound on the deviation probability of the sum from its mean is obtained, as well as a bound on uniform deviation probability.
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https://hal.archives-ouvertes.fr/hal-03175697
Contributor : Emmanuel Gobet <>
Submitted on : Wednesday, April 21, 2021 - 11:36:05 PM
Last modification on : Saturday, July 3, 2021 - 3:46:19 AM

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  • HAL Id : hal-03175697, version 2

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Linda Chamakh, Emmanuel Gobet, Wenjun Liu. Orlicz norms and concentration inequalities for β-heavy tailed random variables. 2021. ⟨hal-03175697v2⟩

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