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Compatibility of conditionally specified models

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  • Chen, Hua Yun

Abstract

A conditionally specified joint model is convenient to use in fields such as spatial data modeling, Gibbs sampling, and missing data imputation. One potential problem with such an approach is that the conditionally specified models may be incompatible, which can lead to serious problems in applications. We propose an odds ratio representation of a joint density to study the issue and derive conditions under which conditionally specified distributions are compatible and yield a joint distribution. Our conditions are the simplest to verify compared with those proposed in the literature. The proposal also explicitly constructs joint densities that are fully compatible with the conditionally specified densities when the conditional densities are compatible, and partially compatible with the conditional densities when they are incompatible. The construction result is then applied to checking the compatibility of the conditionally specified models. Ways to modify the conditionally specified models based on the construction of the joint models are also discussed when the conditionally specified models are incompatible.

Suggested Citation

  • Chen, Hua Yun, 2010. "Compatibility of conditionally specified models," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 670-677, April.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:7-8:p:670-677
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    References listed on IDEAS

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    1. Arnold, Barry C. & Gokhale, D. V., 1994. "On uniform marginal representation of contingency tables," Statistics & Probability Letters, Elsevier, vol. 21(4), pages 311-316, November.
    2. Hua Yun Chen, 2007. "A Semiparametric Odds Ratio Model for Measuring Association," Biometrics, The International Biometric Society, vol. 63(2), pages 413-421, June.
    3. Hua Yun Chen, 2003. "A note on the prospective analysis of outcome‐dependent samples," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 575-584, May.
    4. Yuchung J. Wang & Edward H. Ip, 2008. "Conditionally specified continuous distributions," Biometrika, Biometrika Trust, vol. 95(3), pages 735-746.
    5. Hua Yun Chen, 2004. "Nonparametric and Semiparametric Models for Missing Covariates in Parametric Regression," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1176-1189, December.
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    1. 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.
    2. Hua Yun Chen & Daniel E. Rader & Mingyao Li, 2015. "Likelihood Inferences on Semiparametric Odds Ratio Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1125-1135, September.
    3. Berti, Patrizia & Dreassi, Emanuela & Rigo, Pietro, 2014. "Compatibility results for conditional distributions," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 190-203.
    4. 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.
    5. Dreassi, Emanuela & Rigo, Pietro, 2017. "A note on compatibility of conditional autoregressive models," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 9-16.

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