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2001 A Note on Talagrand's Concentration Inequality
Dmitriy Panchenko
Author Affiliations +
Electron. Commun. Probab. 6: 55-65 (2001). DOI: 10.1214/ECP.v6-1034

Abstract

In this paper we revisit Talagrand's proof of concentration inequality for empirical processes. We give a different proof of the main technical lemma that guarantees the existence of a certain kernel. Moreover, we generalize the result of Talagrand to a family of kernels which in one particular case allows us to produce the Poissonian bound without using the truncation argument. We also give some examples of applications of the abstract concentration inequality to empirical processes that demonstrate some interesting properties of Talagrand's kernel method.

Citation

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Dmitriy Panchenko. "A Note on Talagrand's Concentration Inequality." Electron. Commun. Probab. 6 55 - 65, 2001. https://doi.org/10.1214/ECP.v6-1034

Information

Accepted: 24 April 2001; Published: 2001
First available in Project Euclid: 19 April 2016

zbMATH: 0977.60008
MathSciNet: MR1831801
Digital Object Identifier: 10.1214/ECP.v6-1034

Subjects:
Primary: 60E15
Secondary: 28A35

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