The Annals of Probability

About the constants in Talagrand's concentration inequalities for empirical processes

Pascal Massart

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We propose some explicit values for the constants involved in the exponential concentration inequalities for empirical processes which are due to Talagrand. It has been shown by Ledoux that deviation inequalities for empirical processes could be obtained by iteration of logarithmic Sobolev type inequalities. Our approach follows closely that of Ledoux. The improvements that we get with respect to Ledoux’s work are based on refinements of his entropy inequalities and computations.

Article information

Ann. Probab., Volume 28, Number 2 (2000), 863-884.

First available in Project Euclid: 18 April 2002

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Zentralblatt MATH identifier

Primary: 60E15: Inequalities; stochastic orderings
Secondary: 60F10: Large deviations 94A17

Concentration of measure concentration inequalities deviation inequalities empirical processes


Massart, Pascal. About the constants in Talagrand's concentration inequalities for empirical processes. Ann. Probab. 28 (2000), no. 2, 863--884. doi:10.1214/aop/1019160263.

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