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About the constants in Talagrand’s concentration inequalities for empirical processes. (English) Zbl 1140.60310

Summary: 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 inequalities of logarithmic Sobolev type. Our approach follows closely that of Ledoux. The improvements that we obtain with respect to Ledoux’s work are based on refinements of his entropy inequalities and computations.

MSC:

60E15 Inequalities; stochastic orderings
60F10 Large deviations
94A17 Measures of information, entropy
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