Moment inequalities for functions of independent random variables

Details Moment inequalities for functions of independent random variables Moment inequalities for functions of independent random variables

2005-03-29

arxiv.org/abs/math/0503651v1

Annals of Probability 2005, Vol. 33, No. 2, 514-560

Mathematics

Probability

Published at http://dx.doi.org/10.1214/009117904000000856 in the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

10.1214/009117904000000856

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 Latala 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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