Exponential inequalities for self-normalized martingales with applications
Statistics Theory
2008-11-14 v2 Probability
Statistics Theory
Abstract
We propose several exponential inequalities for self-normalized martingales similar to those established by De la Pe\~{n}a. The keystone is the introduction of a new notion of random variable heavy on left or right. Applications associated with linear regressions, autoregressive and branching processes are also provided.
Cite
@article{arxiv.0707.3715,
title = {Exponential inequalities for self-normalized martingales with applications},
author = {Bernard Bercu and Abderrahmen Touati},
journal= {arXiv preprint arXiv:0707.3715},
year = {2008}
}
Comments
Published in at http://dx.doi.org/10.1214/07-AAP506 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)