Bernstein inequality and moderate deviations under strong mixing conditions

2012/02/21 by Florence Merlevède, Magda Peligrad, Emmanuel Rio · 4 citations
Mathematics · #math.PR #msc:60E15 #msc:60F10 #msc:62G07

paper · pdf

published as IMS Collections, High Dimensional Probability V, (2009), 273-292 · 20 pages

arxiv created 2012/02/21 · arxiv updated 2012/02/23

Abstract

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 coeficients that complements the large deviation result obtained by Bryc and Dembo (1998) under superexponential mixing rates.

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