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Structural decompositions of multivariate distributions with applications in moment and cumulant

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  • Ip, Edward H.
  • Wang, Yuchung J.
  • Yeh, Yeong-nan

Abstract

We provide lattice decompositions for multivariate distributions. The lattice decompositions reveal the structural relationship between the Lancaster/Bahadur model and the model of Streitberg (Ann. Statist. 18 (1990) 1878). For multivariate categorical data, the decompositions allows modeling strategy for marginal inference. The theory discussed in this paper illustrates the concept of reproducibility, which was discussed in Liang et al. (J. Roy. Statist. Soc. Ser. B 54 (1992) 3). For the purpose of delineating the relationship between the various types of decompositions of distributions, we develop a theory of polytypefication, the generality of which is exploited to prove results beyond interaction.

Suggested Citation

  • Ip, Edward H. & Wang, Yuchung J. & Yeh, Yeong-nan, 2004. "Structural decompositions of multivariate distributions with applications in moment and cumulant," Journal of Multivariate Analysis, Elsevier, vol. 89(1), pages 119-134, April.
    • Handle: RePEc:eee:jmvana:v:89:y:2004:i:1:p:119-134
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    References listed on IDEAS

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    1. Teugels, Jozef L, 1990. "Some representations of the multivariate Bernoulli and binomial distributions," Journal of Multivariate Analysis, Elsevier, vol. 32(2), pages 256-268, February.
    2. Jones, M. C., 1998. "Constant Local Dependence," Journal of Multivariate Analysis, Elsevier, vol. 64(2), pages 148-155, February.
    3. Ip, Edward H. & Wang, Yuchung J. & Yeh, Yeong-nan, 2003. "Some equivalence results concerning multiplicative lattice decompositions of multivariate densities," Journal of Multivariate Analysis, Elsevier, vol. 84(2), pages 403-409, February.
    4. Teugels, J. L. & Van Horebeek, J., 1998. "Algebraic Descriptions of Nominal Multivariate Discrete Data," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 203-226, November.
    5. André Carlier & Pieter Kroonenberg, 1996. "Decompositions and biplots in three-way correspondence analysis," Psychometrika, Springer;The Psychometric Society, vol. 61(2), pages 355-373, June.
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    1. Stojan Jovanović & Stefan Rotter, 2016. "Interplay between Graph Topology and Correlations of Third Order in Spiking Neuronal Networks," PLOS Computational Biology, Public Library of Science, vol. 12(6), pages 1-28, June.

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