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Bernstein inequality and moderate deviations under strong mixing conditions

Florence Merlevède, Magda Peligrad, and Emmanuel Rio

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In this paper we obtain a Bernstein type inequality for a class of weakly dependent and bounded random variables. The proofs lead to a moderate deviations principle for sums of bounded random variables with exponential decay of the strong mixing coefficients that complements the large deviation result obtained by Bryc and Dembo (1998) under superexponential mixing rates.

Chapter information

Christian Houdré, Vladimir Koltchinskii, David M. Mason and Magda Peligrad, eds., High Dimensional Probability V: The Luminy Volume (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2009), 273-292

First available in Project Euclid: 2 February 2010

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Zentralblatt MATH identifier

Primary: 60E15: Inequalities; stochastic orderings 60F10: Large deviations 62G07: Density estimation

deviation inequality moderate deviations principle weakly dependent sequences strong mixing

Copyright © 2009, Institute of Mathematical Statistics


Merlevède, Florence; Peligrad, Magda; Rio, Emmanuel. Bernstein inequality and moderate deviations under strong mixing conditions. High Dimensional Probability V: The Luminy Volume, 273--292, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2009. doi:10.1214/09-IMSCOLL518.

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