Exponential inequalities for self-normalized martingales with applications

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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.
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)

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Statistics Theory, Probability, 60E15, 60G42 (Primary) 60G15, 60J80 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/173983

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0707.3715
 http://arxiv.org/abs/0707.3715
 Annals of Applied Probability 2008, Vol. 18, No. 5, 1848-1869
 doi:10.1214/07-AAP506

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arXiv