Hoeffding decompositions and two-colour urn sequences

Omar El-Dakkak (1) , Giovanni Peccati (1)

1 LSTA - Laboratoire de Statistique Théorique et Appliquée

Let X be a non-deterministic infinite exchangeable sequence with values in {0,1}. We show that X is Hoeffding-decomposable if, and only if, X is either an i.i.d. sequence or a Polya sequence. This completes the results established in Peccati [2004]. The proof uses several combinatorial implications of the correspondence between Hoeffding decomposability and weak independence. Our results must be compared with previous characterizations of i.i.d. and Polya sequences given by Hill et al. [1987] and Diaconis and Yilvisaker [1979].

Mots clés: Exchangeable sequences; Hoeffding decompositions; Polya urns; Weak independence

Domaines: Probabilités [math.PR]

Omar El-Dakkak, Giovanni Peccati. Hoeffding decompositions and two-colour urn sequences. 2006. ⟨hal-00107998v2⟩