HOEFFDING DECOMPOSITIONS AND URN SEQUENCES

• 成果类型: Article
• 署名作者: El-Dakkak, Omar; Peccati, Giovanni
• 署名单位: Sorbonne Universite
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/07-AOP389
• 发表日期: 2008
• 页码: 2280-2310
• 关键词: finite population statistics; orthogonal decomposition; symmetric statistics; Edgeworth Expansion; dirichlet processes; REPRESENTATION; functionals

摘要

Let X = (X(1), X(2),...) be a nondeterministic 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 [Ann. Probab. 32 (2004) 1796-1829]. 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 sequence, given by Hill. Lane And Sudderth [Ami. Probab. 15 (1987) 1586-1592] and Diaconis and Ylvisaker [Ann. Statist. 7 (1979) 269-281]. The final section contains a partial characterization of Hoeffding decomposable sequences with values in a set with more than two elements.