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November 2008 Hoeffding decompositions and urn sequences
Omar El-Dakkak, Giovanni Peccati
Ann. Probab. 36(6): 2280-2310 (November 2008). DOI: 10.1214/07-AOP389


Let X=(X1, X2, …) 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 Pólya 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 Pólya sequences given by Hill, Lane and Sudderth [Ann. 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.


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Omar El-Dakkak. Giovanni Peccati. "Hoeffding decompositions and urn sequences." Ann. Probab. 36 (6) 2280 - 2310, November 2008.


Published: November 2008
First available in Project Euclid: 19 December 2008

zbMATH: 1163.60015
MathSciNet: MR2478683
Digital Object Identifier: 10.1214/07-AOP389

Primary: 60G09 , 60G99

Keywords: exchangeable sequences , Hoeffding decompositions , Pólya urns , weak independence

Rights: Copyright © 2008 Institute of Mathematical Statistics


Vol.36 • No. 6 • November 2008
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