Doukhan and Louhichi introduced a covariance-based concept of weak dependence which is more general than classical mixing concepts. We prove a Bernstein-type inequality under this condition which is similar to the well-known inequality in the independent case. We apply this tool to derive asymptotic properties of penalized least-squares estimators in Barron's classes.
Publié le : 2006-04-14
Classification:
Barron's classes,
Bernstein-type inequality,
cumulants,
neural networks,
nonparametric autoregression,
penalized least squares,
weak dependence
@article{1145993977,
author = {Kallabis, Raoul S. and Neumann, Michael H.},
title = {An exponential inequality under weak dependence},
journal = {Bernoulli},
volume = {12},
number = {2},
year = {2006},
pages = { 333-350},
language = {en},
url = {http://dml.mathdoc.fr/item/1145993977}
}
Kallabis, Raoul S.; Neumann, Michael H. An exponential inequality under weak dependence. Bernoulli, Tome 12 (2006) no. 2, pp. 333-350. http://gdmltest.u-ga.fr/item/1145993977/