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Compatibility results for conditional distributions

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  • Berti, Patrizia
  • Dreassi, Emanuela
  • Rigo, Pietro

Abstract

In various frameworks, to assess the joint distribution of a k-dimensional random vector X=(X1,…,Xk), one selects some putative conditional distributions Q1,…,Qk. Each Qi is regarded as a possible (or putative) conditional distribution for Xi given (X1,…,Xi−1,Xi+1,…,Xk). The Qi are compatible if there is a joint distribution P for X with conditionals Q1,…,Qk. Three types of compatibility results are given in this paper. First, the Xi are assumed to take values in compact subsets of R. Second, the Qi are supposed to have densities with respect to reference measures. Third, a stronger form of compatibility is investigated. The law P with conditionals Q1,…,Qk is requested to belong to some given class P0 of distributions. Two choices for P0 are considered, that is, P0={exchangeable laws} and P0={laws with identical univariate marginals}.

Suggested Citation

  • Berti, Patrizia & Dreassi, Emanuela & Rigo, Pietro, 2014. "Compatibility results for conditional distributions," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 190-203.
    • Handle: RePEc:eee:jmvana:v:125:y:2014:i:c:p:190-203
    DOI: 10.1016/j.jmva.2013.12.009
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    References listed on IDEAS

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    1. Kaiser, Mark S. & Cressie, Noel, 2000. "The Construction of Multivariate Distributions from Markov Random Fields," Journal of Multivariate Analysis, Elsevier, vol. 73(2), pages 199-220, May.
    2. Ip, Edward H. & Wang, Yuchung J., 2009. "Canonical representation of conditionally specified multivariate discrete distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1282-1290, July.
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    4. Chen, Hua Yun, 2010. "Compatibility of conditionally specified models," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 670-677, April.
    5. Yuchung J. Wang & Edward H. Ip, 2008. "Conditionally specified continuous distributions," Biometrika, Biometrika Trust, vol. 95(3), pages 735-746.
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    Cited by:

    1. 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.
    2. Dreassi, Emanuela & Rigo, Pietro, 2017. "A note on compatibility of conditional autoregressive models," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 9-16.
    3. Patrizia Berti & Luca Pratelli & Pietro Rigo, 2014. "A unifying view on some problems in probability and statistics," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(4), pages 483-500, November.
    4. Patrizia Berti & Emanuela Dreassi & Pietro Rigo, 2020. "A notion of conditional probability and some of its consequences," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(1), pages 3-15, June.
    5. Linda Khachatryan & Boris S. Nahapetian, 2023. "On the Characterization of a Finite Random Field by Conditional Distribution and its Gibbs Form," Journal of Theoretical Probability, Springer, vol. 36(3), pages 1743-1761, September.
    6. Barry C. Arnold & B. G. Manjunath, 2022. "All Conditional Distributions for Y Given X that are Compatible with a Given Conditional Distribution for X Given Y," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 419-426, August.
    7. Arnold, Barry C. & Sarabia, José María, 2022. "Conditional specification of statistical models: Classical models, new developments and challenges," Journal of Multivariate Analysis, Elsevier, vol. 188(C).

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