Electronic Journal of Probability

On concentration of self-bounding functions

Stephane Boucheron, Gabor Lugosi, and Pascal Massart

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Abstract

We prove some new concentration inequalities for self-bounding functions using the entropy method. As an application, we recover Talagrand's convex distance inequality. The new Bernstein-like inequalities for self-bounding functions are derived thanks to a careful analysis of the so-called Herbst argument. The latter involves comparison results between solutions of differential inequalities that may be interesting in their own right.

Article information

Source
Electron. J. Probab., Volume 14 (2009), paper no. 64, 1884-1899.

Dates
Accepted: 9 September 2009
First available in Project Euclid: 1 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464819525

Digital Object Identifier
doi:10.1214/EJP.v14-690

Mathematical Reviews number (MathSciNet)
MR2540852

Zentralblatt MATH identifier
1189.60040

Subjects
Primary: 60E15: Inequalities; stochastic orderings 60C05: Combinatorial probability 28A35: Measures and integrals in product spaces
Secondary: 05C80: Random graphs [See also 60B20]

Keywords
concentration inequality convex distance self-bounding function

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

Citation

Boucheron, Stephane; Lugosi, Gabor; Massart, Pascal. On concentration of self-bounding functions. Electron. J. Probab. 14 (2009), paper no. 64, 1884--1899. doi:10.1214/EJP.v14-690. https://projecteuclid.org/euclid.ejp/1464819525


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References

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