A moderate deviation for associated random variables

Moderate deviations are an important topic in many theoretical or applied statistical areas. We prove two versions of a moderate deviation for associated and strictly stationary random variables with finite moments of order q>2. The first one uses an assumption depending on the rate of a Gaussian...

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Bibliographic Details
Published in:Journal of the Korean Statistical Society 2016, 45(2), , pp.285-294
Main Authors: Çaǧın, Tonguç, Oliveira, Paulo Eduardo, Torrado, Nuria
Format: Article
Language:English
Subjects:
Applied Statistics
Approximation
Association
Bayesian Inference
Coupling
Moderate deviation
Statistical Theory and Methods
Statistics
Statistics and Computing/Statistics Programs
통계학
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Summary:Moderate deviations are an important topic in many theoretical or applied statistical areas. We prove two versions of a moderate deviation for associated and strictly stationary random variables with finite moments of order q>2. The first one uses an assumption depending on the rate of a Gaussian approximation, while the second one discusses more natural assumptions to obtain the approximation rate. The control of the dependence structure relies on the decay rate of the covariances, for which we assume a relatively mild polynomial decay rate. The proof combines a coupling argument together with a suitable use of Berry–Esséen bounds.
ISSN:1226-3192
2005-2863
DOI:10.1016/j.jkss.2015.11.004