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Pré-Publication, Document De Travail Année : 2021

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

Résumé

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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Dates et versions

hal-03175697 , version 1 (20-03-2021)
hal-03175697 , version 2 (21-04-2021)
hal-03175697 , version 3 (30-06-2021)

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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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