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Exchangeable Hoeffding decompositions over finite sets: A combinatorial characterization and counterexamples

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  • El-Dakkak, Omar
  • Peccati, Giovanni
  • Prünster, Igor

Abstract

We study Hoeffding decomposable exchangeable sequences with values in a finite set D={d1,…,dK}. We provide a new combinatorial characterization of Hoeffding decomposability and use this result to show that, for every K≥3, there exists a class of neither Pólya nor i.i.d. D-valued exchangeable sequences that are Hoeffding decomposable.

Suggested Citation

  • El-Dakkak, Omar & Peccati, Giovanni & Prünster, Igor, 2014. "Exchangeable Hoeffding decompositions over finite sets: A combinatorial characterization and counterexamples," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 51-64.
    • Handle: RePEc:eee:jmvana:v:131:y:2014:i:c:p:51-64
    DOI: 10.1016/j.jmva.2014.04.012
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    References listed on IDEAS

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    1. Vitale, Richard A., 1992. "Covariances of symmetric statistics," Journal of Multivariate Analysis, Elsevier, vol. 41(1), pages 14-26, April.
    2. Lancelot F. James & Antonio Lijoi & Igor Prünster, 2006. "Conjugacy as a Distinctive Feature of the Dirichlet Process," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(1), pages 105-120, March.
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