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Concentration Inequalities for Sub-Additive Functions Using the Entropy Method




We obtain exponential concentration inequalities for sub-additive functions of independent random variables under weak conditions on the increments of those functions, like the existence of exponential moments for these increments. As a consequence of these general inequalities, we obtain refinements of Talagrand's inequality for empirical processes and new bounds for randomized empirical processes. These results are obtained by further developing the entropy method introduced by Ledoux.

Author(s): Bousquet, O.
Journal: Stochastic Inequalities and Applications
Volume: 56
Pages: 213-247
Year: 2003
Month: November
Day: 0
Series: Progress in Probability
Editors: Giné, E., C. Houdré and D. Nualart

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

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

Links: PostScript


  title = {Concentration Inequalities for Sub-Additive Functions Using the Entropy Method},
  author = {Bousquet, O.},
  journal = {Stochastic Inequalities and Applications},
  volume = {56},
  pages = {213-247},
  series = {Progress in Probability},
  editors = {Giné, E., C. Houdré and D. Nualart},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  month = nov,
  year = {2003},
  month_numeric = {11}