Electronic Journal of Probability

On concentration of self-bounding functions

Stephane Boucheron, Gabor Lugosi, and Pascal Massart

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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

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

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

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Zentralblatt MATH identifier

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

concentration inequality convex distance self-bounding function

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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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