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Moment Inequalities for Functions of Independent Random Variables




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 cite{BoLuMa01}, 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.

Author(s): Boucheron, S. and Bousquet, O. and Lugosi, G. and Massart, P.
Journal: To appear in Annals of Probability
Volume: 33
Pages: 514-560
Year: 2005
Day: 0

Department(s): Empirical Inference
Bibtex Type: Article (article)

Digital: 0
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

Links: PDF


  title = {Moment Inequalities for Functions of Independent Random Variables},
  author = {Boucheron, S. and Bousquet, O. and Lugosi, G. and Massart, P.},
  journal = {To appear in Annals of Probability},
  volume = {33},
  pages = {514-560},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  year = {2005}