Hoeffding-Type Concentration Bounds for Exchangeable Random Variables

Abstract

We establish Hoeffding-type concentration inequalities for empirical means of bounded infinitely exchangeable sequences. Using the unique de Finetti mixing measure, we identify the appropriate concentration set as the collection of means of the component distributions in the support of the mixing law. The empirical mean concentrates exponentially around this set, with the same exponential rate as in the classical Hoeffding inequality. More sharply, the empirical mean concentrates directly around its random almost sure de Finetti limit. This also yields one sided bounds relative to the smallest and largest component means. When the mixing measure is concentrated at a single distribution, the sequence is independent and identically distributed, and our result recovers the classical Hoeffding inequality.