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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.
@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} }