We propose some explicit values for the constants involved in the
exponential concentration inequalities for empirical processes which are due to
Talagrand. It has been shown by Ledoux that deviation inequalities for
empirical processes could be obtained by iteration of logarithmic Sobolev type
inequalities. Our approach follows closely that of Ledoux. The improvements
that we get with respect to Ledoux’s work are based on refinements of
his entropy inequalities and computations.
Publié le : 2000-04-14
Classification:
Concentration of measure,
concentration inequalities,
deviation inequalities,
empirical processes,
60E15,
60F10,
94A17
@article{1019160263,
author = {Massart, Pascal},
title = {About the constants in Talagrand's concentration inequalities for
empirical processes},
journal = {Ann. Probab.},
volume = {28},
number = {1},
year = {2000},
pages = { 863-884},
language = {en},
url = {http://dml.mathdoc.fr/item/1019160263}
}
Massart, Pascal. About the constants in Talagrand's concentration inequalities for
empirical processes. Ann. Probab., Tome 28 (2000) no. 1, pp. 863-884. http://gdmltest.u-ga.fr/item/1019160263/