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Exponential inequalities for martingales with applications

Abstract : The paper is devoted to establishing some general exponential inequalities for super-martingales. The inequalities improve or generalize many exponential inequalities of Bennett, Freedman, de la Peña, Pinelis and van de Geer. Moreover, our concentration inequalities also improve some known inequalities for sums of independent random variables. Applications associated with linear regressions, autoregressive processes and branching processes are provided. In particular, an interesting application of de la Peña's inequality to self-normalized deviations is also provided.
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Submitted on : Thursday, January 22, 2015 - 9:49:34 AM
Last modification on : Saturday, June 25, 2022 - 7:45:59 PM
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Xiequan Fan, Ion Grama, Quansheng Liu. Exponential inequalities for martingales with applications. Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2015, 20, pp.1 - 22. ⟨10.1214/EJP.v20-3496⟩. ⟨hal-01108032⟩



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