Concentration for independent random variables with heavy tails

By Franck Barthe, Patrick Cattiaux, Cyril Roberto. 2005

59 citations recorded by the source corpus.

If a random variable is not exponentially integrable, it is known that no concentration inequality holds for an infinite sequence of independent copies. Under mild conditions, we establish concentration inequalities for finite sequences of $n$ independent copies, with good dependence in $n$.

Subfields: Management Science and Operations Research, Numerical Analysis, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/c8b5bcc37017075eff4fcdf3fa9908b2e6a7e691

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In Management Science and Operations Research

In Numerical Analysis

In Statistics and Probability

Citations in the corpus

Orlicz–Sobolev inequalities for sub-Gaussian measures and ergodicity of Markov semi-groups☆ (2006, background): “For other directions on the study of sub-Gaussian measures, the reader could like to see also [GGM05, BCR05a , BCR05c, Zeg01].”
Applications of Stein's method for concentration inequalities (2009, background): “The papers [2, 14, 20, 28] deal with tails between exponential and Gaussian and [1, 4] deal with subexponential tails.”
Functional Inequalities for Heavy Tailed Distributions and Application to Isoperimetry (2010, methodology): “Some bounds on Iμn , not optimal in n, are obtained in [9] using weak Poincaré inequality.”
Rate of convergence for ergodic continuous Markov processes : Lyapunov versus Poincaré (2007, methodology): “The sharp result in dimension 1 has been given in [3] with βp(s) = dps −2/p, but cannot be extended to higher dimensions.”
Central limit theorems for additive functionals of ergodic Markov diffusions processes (2011, background): “t explicit convergence controls are Lyapunov conditions as explained before. 5.3. Reversible case in dimension one. 5.3.1. General criterion for weak Poincar´e inequalities. We recall here results of [BCR05] giving necessary and suﬃcient conditions for a one dimensional measure dµ(x) = e−V (x)dx, as”