Exponential inequalities for self-normalized martingales with applications

Authors
Bercu, Bernard Touati, Abderrahmen
Citation
Bercu, Bernard et Touati, Abderrahmen, Exponential inequalities for self-normalized martingales with applications, Annals of applied probability , 18(5), 2008, pp. 1848-1869
Journal title
Annals of applied probability → ACNP
ISSN journal
10505164
Volume
18
Issue
5
Year of publication
2008
Pages
1848 - 1869
Database
ACNP
SICI code
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.