Electronic Journal of Probability
- Electron. J. Probab.
- Volume 14 (2009), paper no. 64, 1884-1899.
On concentration of self-bounding functions
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.
Electron. J. Probab., Volume 14 (2009), paper no. 64, 1884-1899.
Accepted: 9 September 2009
First available in Project Euclid: 1 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
This work is licensed under aCreative Commons Attribution 3.0 License.
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