The Annals of Probability

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

Pascal Massart

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Abstract

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

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

Dates
First available in Project Euclid: 18 April 2002

Permanent link to this document
http://projecteuclid.org/euclid.aop/1019160263

Mathematical Reviews number (MathSciNet)
MR1782276

Digital Object Identifier
doi:10.1214/aop/1019160263

Zentralblatt MATH identifier
01905939

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

Keywords
Concentration of measure concentration inequalities deviation inequalities empirical processes

Citation

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. http://projecteuclid.org/euclid.aop/1019160263.


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