Bernstein inequality and moderate deviations under strong mixing conditions

Florence Merlevède (1) , Magda Peligrad (2) , Emmanuel Rio (3, 4)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
2 Department of Mathematical Sciences [Cincinnati]
3 LMV - Laboratoire de Mathématiques de Versailles
4 CQFD - Quality control and dynamic reliability

In this paper we obtain a Bernstein type inequality for geometrically strongly mixing sequences of bounded random variables. This inequality leads to a moderate deviations prinicple that complements the large deviation result obtained by Bryc and Dembo (1998) under superexponential mixing rates.

Mots clés: Deviation inequality; moderate deviations principle; weakly dependent sequences; strong mixing; density estimation

Domaines: Probabilités [math.PR]

Florence Merlevède, Magda Peligrad, Emmanuel Rio. Bernstein inequality and moderate deviations under strong mixing conditions. High dimensional probability V : the 5th International Conference (HDP V), May 2008, Luminy, France. pp.273-292. ⟨inria-00360856⟩