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Robust Bayesian Inference for Seemingly Unrelated Regressions with Elliptical Errors

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  • Ng, Vee Ming

Abstract

Bayesian inference is considered for the seemingly unrelated regressions with an elliptically contoured error distribution. We show that the posterior distribution of the regression parameters and the predictive distribution of future observations under elliptical errors assumption are identical to those obtained under independently distributed normal errors when an improper prior is used. This gives inference robustness with respect to departures from the reference case of independent sampling from the normal distribution.

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  • Ng, Vee Ming, 2002. "Robust Bayesian Inference for Seemingly Unrelated Regressions with Elliptical Errors," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 409-414, November.
    • Handle: RePEc:eee:jmvana:v:83:y:2002:i:2:p:409-414
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    References listed on IDEAS

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    1. Chib, Siddhartha & Tiwari, Ram C. & Jammalamadaka, S. Rao, 1988. "Bayes prediction in regressions with elliptical errors," Journal of Econometrics, Elsevier, vol. 38(3), pages 349-360, July.
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    Cited by:

    1. Shun Matsuura & Hiroshi Kurata, 2022. "Optimal estimator under risk matrix in a seemingly unrelated regression model and its generalized least squares expression," Statistical Papers, Springer, vol. 63(1), pages 123-141, February.
    2. Arellano-Valle, R.B. & del Pino, G. & Iglesias, P., 2006. "Bayesian inference in spherical linear models: robustness and conjugate analysis," Journal of Multivariate Analysis, Elsevier, vol. 97(1), pages 179-197, January.
    3. Chamberlain Mbah & Kris Peremans & Stefan Van Aelst & Dries F. Benoit, 2019. "Robust Bayesian seemingly unrelated regression model," Computational Statistics, Springer, vol. 34(3), pages 1135-1157, September.
    4. Kibria, B.M. Golam, 2006. "The matrix-t distribution and its applications in predictive inference," Journal of Multivariate Analysis, Elsevier, vol. 97(3), pages 785-795, March.
    5. Zellner, Arnold & Ando, Tomohiro, 2010. "Bayesian and non-Bayesian analysis of the seemingly unrelated regression model with Student-t errors, and its application for forecasting," International Journal of Forecasting, Elsevier, vol. 26(2), pages 413-434, April.
    6. Zellner, Arnold & Ando, Tomohiro, 2010. "A direct Monte Carlo approach for Bayesian analysis of the seemingly unrelated regression model," Journal of Econometrics, Elsevier, vol. 159(1), pages 33-45, November.
    7. Cai, Bo & Dunson, David B., 2007. "Bayesian Multivariate Isotonic Regression Splines: Applications to Carcinogenicity Studies," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1158-1171, December.
    8. Liu, Jin Shan & Ip, Wai Cheung & Wong, Heung, 2009. "Predictive inference for singular multivariate elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1440-1446, August.
    9. Xu, Qinfeng & You, Jinhong & Zhou, Bin, 2008. "Seemingly unrelated nonparametric models with positive correlation and constrained error variances," Economics Letters, Elsevier, vol. 99(2), pages 223-227, May.
    10. Radhey S. Singh & Lichun Wang, 2012. "A Note on Estimation in Seemingly Unrelated Semi-Parametric Regression Models," Journal of Quantitative Economics, The Indian Econometric Society, vol. 10(1), pages 56-69, January.
    11. Shun Matsuura & Hiroshi Kurata, 2020. "Covariance matrix estimation in a seemingly unrelated regression model under Stein’s loss," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(1), pages 79-99, March.

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