Open Access
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


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.


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

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

Keywords: concentration inequality , convex distance , self-bounding function

Vol.14 • 2009
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