Redundancy of exchangeable estimators

Exchangeable random partition processes provide a framework for statistical inference in large alphabet scenarios from a Bayesian perspective. On the other hand, the notion of the pattern of a sequence provides a framework for data compression in large alphabet scenarios. Owing to the relationship between data compression and parameter estimation, both these approaches are related. Motivated by the possibilities of cross-fertilization, we examine the redundancy of Bayes estimators (specifically those that emerge from the “Chinese restaurant processes”) in the setting of unknown discrete alphabets from a universal compression point of view. In particular, we identify relations between alphabet sizes and sample sizes where the redundancy is small- and hence, characterize useful regimes for these estimators.