Asymptotic predictive inference with exchangeable data

Let (Xn) be a sequence of random variables, adapted to a filtration (Gn), and let (Formula Presented) be the empirical and the predictive measures. We focus on (Formula Presented) where D is a class of measurable sets. Conditions for (Formula Presented), almost surely or in probability, are given. Also, to determine the rate of convergence, the asymptotic behavior of rn||μn-an|| is investigated for suitable constants rn. Special attention is paid to rn = √n and (Formula Presented). The sequence (Xn) is exchangeable or, more generally, conditionally identically distributed.