Sufficient conditions, which under weak additional assumptions are also necessary, are found for the central limit theorem for empirical processes indexed by classes of functions which have the Vapnik-Cervonenkis property. This improves an earlier theorem of Pollard (1982a), and leads to necessary and sufficient conditions for the CLT for weighted empirical processes indexed by Vapnik-Cervonenkis classes of sets.
Publié le : 1987-01-14
Classification:
Empirical process,
central limit theorem,
Vapnik-Cervonenkis class,
metric entropy,
weighted empirical process,
60F05,
60F17,
60B12
@article{1176992263,
author = {Alexander, Kenneth S.},
title = {The Central Limit Theorem for Empirical Processes on Vapnik-Cervonenkis Classes},
journal = {Ann. Probab.},
volume = {15},
number = {4},
year = {1987},
pages = { 178-203},
language = {en},
url = {http://dml.mathdoc.fr/item/1176992263}
}
Alexander, Kenneth S. The Central Limit Theorem for Empirical Processes on Vapnik-Cervonenkis Classes. Ann. Probab., Tome 15 (1987) no. 4, pp. 178-203. http://gdmltest.u-ga.fr/item/1176992263/