Moment Inequalities for Functions of Independent Random Variables

Boucheron, S; Bousquet, O; Lugosi, G; Massart, P

doi:10.1214/009117904000000856

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Moment Inequalities for Functions of Independent Random Variables

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

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https://www.jstor.org/stable/3481746
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Citation

Boucheron, S., Bousquet, O., Lugosi, G., & Massart, P. (2005). Moment Inequalities for Functions of Independent Random Variables. Annals of Probability, 33(2), 514-560. doi:10.1214/009117904000000856.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-D6B1-6

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 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.