Exponential inequalities for self-normalized martingales with applications
Authors:
- Bernard BercuBBBernard Bercu
- Abderrahmen TouatiATAbderrahmen Touati
Open Access
- 1 October 2008
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Applied Probability
- Vol. 18 (5) , 1848-1869
Abstract
We propose several exponential inequalities for self-normalized martingales similar to those established by De la Peña. 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.Keywords
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