Large Deviations for Exchangeable Random Vectors
Large Deviations for Exchangeable Random Vectors
Say that a family $\{P_\theta^n: \theta \in \Theta\}$ of sequences of probability measures is exponentially continuous if whenever $\theta_n \rightarrow \theta$, the sequence $\{P_{\theta_n}^n\}$ satisfies a large deviation principle with rate function $\lambda_\theta$. If $\Theta$ is compact and $\{P_\theta^n\}$ is exponentially continuous, then the mixture $P^n(A) =: \int_\Theta P_\theta^n(A)d\mu(\theta)$ satisfies …