Bernstein inequality and moderate deviations under strong mixing conditions. (English) Zbl 1243.60019

Houdré, Christian (ed.) et al., High dimensional probability. V: The Luminy volume. Most papers based on the presentations at the conference (HDP V), Luminy, France, May 26–30, 2008. Beachwood, OH: IMS, Institute of Mathematical Statistics (ISBN 978-0-940600-78-2). Institute of Mathematical Statistics Collections 5, 273-292 (2009).
Summary: 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 W. Bryc and A. Dembo [Ann. Inst. Henri Poincaré, Probab. Stat. 32, No. 4, 549–569 (1996; Zbl 0863.60028)] under superexponential mixing rates.
For the entire collection see [Zbl 1228.60006].


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


Zbl 0863.60028
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