Dinwoodie, I. H.; Zabell, S. L. Large deviations for exchangeable random vectors. (English) Zbl 0760.60025 Ann. Probab. 20, No. 3, 1147-1166 (1992). Let \(\{P_ \theta^ n\): \(\theta\in\Theta\}\) be a sequence of probability measures satisfying a large deviation principle if whenever \(\theta_ n\to\theta\) with rate function \(\lambda_ \theta\). It is proved that the mixture \(P^ n(A)=\int_ \Theta P_ \theta^ n(A)d\mu(\theta)\) satisfies a large deviation principle with rate function \(\lambda(x)=\inf_ \theta\{\lambda_ \theta(x)\}\). The lower and upper bounds for large deviation of the sample means of an infinitely exchangeable sequence are derived. The resulting rate functions are typically nonconvex. Reviewer: A.Plikusas (Vilnius) Cited in 3 ReviewsCited in 25 Documents MSC: 60F10 Large deviations 60F20 Zero-one laws Keywords:exchangeable sequence; large deviation principle; rate function; infinitely exchangeable PDFBibTeX XMLCite \textit{I. H. Dinwoodie} and \textit{S. L. Zabell}, Ann. Probab. 20, No. 3, 1147--1166 (1992; Zbl 0760.60025) Full Text: DOI