Exponential inequalities for self-normalized martingales with applications

Bernard Bercu 1, 2 Abderrahmen Touati 1
2 CQFD - Quality control and dynamic reliability
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : We propose several exponential inequalities for self-normalized martingales similar to those established by De la Pena. 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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  • HAL Id : hal-00165219, version 1
  • ARXIV : 0707.3715

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Bernard Bercu, Abderrahmen Touati. Exponential inequalities for self-normalized martingales with applications. Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 2008, 18, pp.1848-1869. ⟨hal-00165219⟩

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