Characterization of Exchangeable Hoeffding-decomposable Sequences

Abstract

Hoeffding decomposition is a classical method for studying symmetric statistics based on i.i.d. observations. The notion was extended by G. Peccati [Ann. Probab. 32 (2004) 1796–1829] under exchangeability, but apart from a few notable examples, the question of which exchangeable processes are Hoeffding-decomposable remains open. In this note, we announce a complete characterization of the class of exchangeable Hoeffding-decomposable processes in terms of their predictive distributions. As a result, we show that they are connected to exchangeable measure-valued Pólya urn sequences, from which we derive the general form of their prior distributions.