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Bayesian marginal equivalence of elliptical regression models

  • Osiewalski, Jacek
  • Steel, Mark F. J.

The use of proper prior densities in regression models with multivariate non-Normal elliptical error distributions is examined when the scale matrix is known up to a precision factor T, treated as a nuisance parameter. Marginally equivalent models preserve the convenient predictive and posterior results on the parameter of interest B obtained in the reference case of the Normal model and its conditionally natural conjugate gamma prior. Prior densities inducing this property are derived for two special cases of non-Normal elliptical densities representing very different patterns of tail behavior. In a linear framework, so-called semi-conjugate prior structures are defined as leading to marginal equivalence to a Normal data density with a fully natural conjugate prior.

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File URL: http://www.sciencedirect.com/science/article/pii/0304-4076(93)90032-Z
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Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 59 (1993)
Issue (Month): 3 (October)
Pages: 391-403

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Handle: RePEc:eee:econom:v:59:y:1993:i:3:p:391-403
Contact details of provider: Web page: http://www.elsevier.com/locate/jeconom

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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.
  2. Jammalamadaka, S. Rao & Tiwari, Ram C. & Chib, Siddhartha, 1987. "Bayes prediction in the linear model with spherically symmetric errors," Economics Letters, Elsevier, vol. 24(1), pages 39-44.
  3. Osiewalski, Jacek, 1991. "A note on Bayesian inference in a regression model with elliptical errors," Journal of Econometrics, Elsevier, vol. 48(1-2), pages 183-193.
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