Electronic Communications in Probability

A Note on Talagrand's Concentration Inequality

Dmitriy Panchenko

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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.

Article information

Source
Electron. Commun. Probab., Volume 6 (2001), paper no. 5, 55-65.

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1461097550

Digital Object Identifier
doi:10.1214/ECP.v6-1034

Mathematical Reviews number (MathSciNet)
MR1831801

Zentralblatt MATH identifier
0977.60008

Subjects
Primary: 60E15: Inequalities; stochastic orderings
Secondary: 28A35: Measures and integrals in product spaces

Keywords
Concentration of measure empirical processes

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Panchenko, Dmitriy. A Note on Talagrand's Concentration Inequality. Electron. Commun. Probab. 6 (2001), paper no. 5, 55--65. doi:10.1214/ECP.v6-1034. https://projecteuclid.org/euclid.ecp/1461097550


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