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2009 On concentration of self-bounding functions
Stephane Boucheron, Gabor Lugosi, Pascal Massart
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Electron. J. Probab. 14: 1884-1899 (2009). DOI: 10.1214/EJP.v14-690

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.

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Stephane Boucheron. Gabor Lugosi. Pascal Massart. "On concentration of self-bounding functions." Electron. J. Probab. 14 1884 - 1899, 2009. https://doi.org/10.1214/EJP.v14-690

Information

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

zbMATH: 1189.60040
MathSciNet: MR2540852
Digital Object Identifier: 10.1214/EJP.v14-690

Subjects:
Primary: 28A35, 60C05, 60E15
Secondary: 05C80

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