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Bayesian Marginal Equivalence of Elliptical Regression Models

  • Osiewalski, J.
  • Steel, M.

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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Paper provided by Tilburg - Center for Economic Research in its series Papers with number 9119.

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Length: 17 pages
Date of creation: 1991
Date of revision:
Handle: RePEc:fth:tilbur:9119
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TILBURG UNIVERSITY, CENTER FOR ECONOMIC RESEARCH, 5000 LE TILBURG THE NETHERLANDS.

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  1. 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.
  2. 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.
  3. Osiewalski, J., 1989. "A Note On Bayesian Inference In A Regression Model With Elliptical Errors," CORE Discussion Papers 1989040, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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