Hoeffding decompositions and two-colour urn sequences

Details Hoeffding decompositions and two-colour urn sequences Hoeffding decompositions and two-colour urn sequences

2006-10-19

arxiv.org/abs/math/0610590v2

Mathematics

Probability

13 pages; some minor typographical improvements

Scientific paper

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].

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