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Exactly and almost compatible joint distributions for high-dimensional discrete conditional distributions

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  • Kuo, Kun-Lin
  • Song, Chwan-Chin
  • Jiang, Thomas J.

Abstract

A conditional model is a set of conditional distributions, which may be compatible or incompatible, depending on whether or not there exists a joint distribution whose conditionals match the given conditionals. In this paper, we propose a new mathematical tool called a “structural ratio matrix” (SRM) to develop a unified compatibility approach for discrete conditional models. With this approach, we can find all joint pdfs after confirming that the given model is compatible. In practice, it is most likely that the conditional models we encounter are incompatible. Therefore, it is important to investigate approximated joint distributions for them. We use the concept of SRM again to construct an almost compatible joint distribution, with consistency property, to represent the given incompatible conditional model.

Suggested Citation

  • Kuo, Kun-Lin & Song, Chwan-Chin & Jiang, Thomas J., 2017. "Exactly and almost compatible joint distributions for high-dimensional discrete conditional distributions," Journal of Multivariate Analysis, Elsevier, vol. 157(C), pages 115-123.
    • Handle: RePEc:eee:jmvana:v:157:y:2017:i:c:p:115-123
    DOI: 10.1016/j.jmva.2017.03.005
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    References listed on IDEAS

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    1. Wang, Yuchung J. & Kuo, Kun-Lin, 2010. "Compatibility of discrete conditional distributions with structural zeros," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 191-199, January.
    2. Barry Arnold & D. Gokhale, 1998. "Distributions most nearly compatible with given families of conditional distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 7(2), pages 377-390, December.
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    4. Yao, Yi-Ching & Chen, Shih-chieh & Wang, Shao-Hsuan, 2014. "On compatibility of discrete full conditional distributions: A graphical representation approach," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 1-9.
    5. Arnold, Barry C. & Castillo, Enrique & Sarabia, Jose Maria, 2002. "Exact and near compatibility of discrete conditional distributions," Computational Statistics & Data Analysis, Elsevier, vol. 40(2), pages 231-252, August.
    6. Kuo, Kun-Lin & Wang, Yuchung J., 2011. "A simple algorithm for checking compatibility among discrete conditional distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(8), pages 2457-2462, August.
    7. Chen, Shyh-Huei & Ip, Edward H. & Wang, Yuchung J., 2011. "Gibbs ensembles for nearly compatible and incompatible conditional models," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1760-1769, April.
    8. Tian, Guo-Liang & Tan, Ming, 2003. "Exact statistical solutions using the inverse Bayes formulae," Statistics & Probability Letters, Elsevier, vol. 62(3), pages 305-315, April.
    9. Berti, Patrizia & Dreassi, Emanuela & Rigo, Pietro, 2014. "Compatibility results for conditional distributions," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 190-203.
    10. Indranil Ghosh & Saralees Nadarajah, 2016. "An alternative approach for compatibility of two discrete conditional distributions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(15), pages 4416-4432, August.
    11. Chen, Hua Yun, 2010. "Compatibility of conditionally specified models," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 670-677, April.
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