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March 2005 Moment inequalities for functions of independent random variables
Stéphane Boucheron, Olivier Bousquet, Gábor Lugosi, Pascal Massart
Ann. Probab. 33(2): 514-560 (March 2005). DOI: 10.1214/009117904000000856

Abstract

A general method for obtaining moment inequalities for functions of independent random variables is presented. It is a generalization of the entropy method which has been used to derive concentration inequalities for such functions [Boucheron, Lugosi and Massart Ann. Probab. 31 (2003) 1583–1614], and is based on a generalized tensorization inequality due to Latała and Oleszkiewicz [Lecture Notes in Math. 1745 (2000) 147–168]. The new inequalities prove to be a versatile tool in a wide range of applications. We illustrate the power of the method by showing how it can be used to effortlessly re-derive classical inequalities including Rosenthal and Kahane–Khinchine-type inequalities for sums of independent random variables, moment inequalities for suprema of empirical processes and moment inequalities for Rademacher chaos and U-statistics. Some of these corollaries are apparently new. In particular, we generalize Talagrand’s exponential inequality for Rademacher chaos of order 2 to any order. We also discuss applications for other complex functions of independent random variables, such as suprema of Boolean polynomials which include, as special cases, subgraph counting problems in random graphs.

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Stéphane Boucheron. Olivier Bousquet. Gábor Lugosi. Pascal Massart. "Moment inequalities for functions of independent random variables." Ann. Probab. 33 (2) 514 - 560, March 2005. https://doi.org/10.1214/009117904000000856

Information

Published: March 2005
First available in Project Euclid: 3 March 2005

zbMATH: 1074.60018
MathSciNet: MR2123200
Digital Object Identifier: 10.1214/009117904000000856

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

Keywords: Concentration inequalities , Empirical processes , Moment inequalities , Random graphs

Rights: Copyright © 2005 Institute of Mathematical Statistics

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Vol.33 • No. 2 • March 2005
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