Empirical Inference Article 2003

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
Bibtex Type: Article (article)
Digital: 0
Electronic Archiving: grant_archive
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik
Links:

BibTex

@article{2079,
  title = {Concentration Inequalities for Sub-Additive Functions Using the Entropy Method},
  journal = {Stochastic Inequalities and Applications},
  abstract = {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.},
  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},
  slug = {2079},
  author = {Bousquet, O.},
  month_numeric = {11}
}