Exponential inequalities for self-normalized martingales with applications

Details Exponential inequalities for self-normalized martingales with applications Exponential inequalities for self-normalized martingales with applications

2007-07-25

arxiv.org/abs/0707.3715v2

Annals of Applied Probability 2008, Vol. 18, No. 5, 1848-1869

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/07-AAP506 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/07-AAP506

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.

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