Large deviations for exchangeable random vectors (Q1201164)

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.