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Moment Inequalities for Functions of Independent Random Variables


Bousquet,  O
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Boucheron, S., Bousquet, O., Lugosi, G., & Massart, P. (2005). Moment Inequalities for Functions of Independent Random Variables. To appear in Annals of Probability, 33, 514-560.

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 citeBoLuMa01}, and is based on a generalized tensorization inequality due to Lata{l}a and Oleszkiewicz cite{LaOl00. 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 Talagrands exponential inequality for Rademacher chaos of order two 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.