Hoeffding decompositions for exchangeable sequences and chaotic representation of functionals of Dirichlet processes. (Q1408178)

An exchangeable sequence of observations \(\{ X_n, 1\leq n\leq N\}\) is Hoeffding decomposable if for each \(n\) every square integrable centered and symmetric functional of \({\mathbf X}_n =(X_1,...,X_n)\) is the orthogonal sum of \(n\) U-statistics with degenerated and symmetric kernels. A necessary and sufficient condition for an exchangeable sequence to be Hoeffding decomposable is given. It is shown that a class of sequences satisfying this condition is given by generalized urn sequences, specifically, by generalized Pólya urns.