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Conditional independence models for seemingly unrelated regressions with incomplete data

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  • Drton, Mathias
  • Andersson, Steen A.
  • Perlman, Michael D.

Abstract

We consider normal [reverse not equivalent] Gaussian seemingly unrelated regressions (SUR) with incomplete data (ID). Imposing a natural minimal set of conditional independence constraints, we find a restricted SUR/ID model whose likelihood function and parameter space factor into the product of the likelihood functions and the parameter spaces of standard complete data multivariate analysis of variance models. Hence, the restricted model has a unimodal likelihood and permits explicit likelihood inference. In the development of our methodology, we review and extend existing results for complete data SUR models and the multivariate ID problem.

Suggested Citation

  • Drton, Mathias & Andersson, Steen A. & Perlman, Michael D., 2006. "Conditional independence models for seemingly unrelated regressions with incomplete data," Journal of Multivariate Analysis, Elsevier, vol. 97(2), pages 385-411, February.
    • Handle: RePEc:eee:jmvana:v:97:y:2006:i:2:p:385-411
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    References listed on IDEAS

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    1. Oksanen, E. H., 1987. "A note on seemingly unrelated regression equations with residual vectors as explanatory variables," Statistics & Probability Letters, Elsevier, vol. 6(2), pages 103-105, November.
    2. Swamy, P. A. V. B. & Mehta, J. S., 1975. "On Bayesian estimation of seemingly unrelated regressions when some observations are missing," Journal of Econometrics, Elsevier, vol. 3(2), pages 157-169, May.
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    4. Hwang, Hae-shin, 1990. "Estimation of a Linear SUR Model with Unequal Numbers of Observations," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 510-515, August.
    5. Andersson, Steen A. & Perlman, Michael D., 1991. "Lattice-ordered conditional independence models for missing data," Statistics & Probability Letters, Elsevier, vol. 12(6), pages 465-486, December.
    6. Andersson, S. A. & Perlman, M. D., 1995. "Testing Lattice Conditional Independence Models," Journal of Multivariate Analysis, Elsevier, vol. 53(1), pages 18-38, April.
    7. Steel, M. A. & Wood, G. R., 1993. "On a problem of Andersson and Perlman," Statistics & Probability Letters, Elsevier, vol. 18(5), pages 381-382, December.
    8. Mathias Drton, 2004. "Multimodality of the likelihood in the bivariate seemingly unrelated regressions model," Biometrika, Biometrika Trust, vol. 91(2), pages 383-392, June.
    9. Andersson, Steen A. & Perlman, Michael D., 1998. "Normal Linear Regression Models With Recursive Graphical Markov Structure," Journal of Multivariate Analysis, Elsevier, vol. 66(2), pages 133-187, August.
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