Yale University
Department of Statistics Seminar

Monday, March 1, 2004

Gabor Lugosi
Department of Economics
Pompeu Fabra University, Barcelona

Title: Moment inequalities for functions of independent random variables
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, and is based on a generalized tensorization inequality due to Latala and Oleszkiewicz. 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 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.
(joint work with S. Boucheron, O. Bousquet, and P. Massart)

Seminar to be held in Room 107, 24 Hillhouse at 4:15 pm

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