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Bayesian marginal equivalence of elliptical regression models

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

Abstract

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 Universidad Carlos III de Madrid in its series Open Access publications from Universidad Carlos III de Madrid with number info:hdl:10016/10950.

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Handle: RePEc:ner:carlos:info:hdl:10016/10950

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Related research

Keywords: Multivariate elliptical data densities; Proper priors; Model robustness; Student t density;

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  1. Osiewalski, J. & Steel, M.F.J., 1990. "Robust Bayesian inference in elliptical regression models," Discussion Paper 1990-32, Tilburg University, Center for Economic Research.
  2. Chib, S. & Osiewalski, J. & Steel, M., 1990. "Posterior Inference On The Degrees Of Freedom Parameter In Multivariate-T Regression Models," Papers 9043, Tilburg - Center for Economic Research.
  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).
  4. 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.
  5. Richard, J. F. & Steel, M. F. J., 1988. "Bayesian analysis of systems of seemingly unrelated regression equations under a recursive extended natural conjugate prior density," Journal of Econometrics, Elsevier, vol. 38(1-2), pages 7-37.
  6. 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.
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Cited by:
  1. 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.
  2. Osiewalski, Jacek & Steel, Mark F.J., . "Robust bayesian inference in empirical regression models," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/2814, Universidad Carlos III de Madrid.
  3. Jacek Osiewalski, 2011. "Bayesian Variations on the Frisch and Waugh Theme," Central European Journal of Economic Modelling and Econometrics, CEJEME, vol. 3(1), pages 39-47, March.

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