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Bayesian Marginal Equivalence of Elliptical Regression Models

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  • Osiewalski, J.
  • Steel, M.

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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Suggested Citation

  • Osiewalski, J. & Steel, M., 1991. "Bayesian Marginal Equivalence of Elliptical Regression Models," Papers 9119, Tilburg - Center for Economic Research.
    • Handle: RePEc:fth:tilbur:9119
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    1. Steel, M.F.J., 1991. "Bayesian inference in time series," Other publications TiSEM 652ec120-1443-4035-9eea-9, Tilburg University, School of Economics and Management.
    2. Steel, M.F.J., 1991. "Bayesian inference in time series," Other publications TiSEM 652ec120-1443-4035-9eea-9, Tilburg University, School of Economics and Management.
    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.
    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. J.‐P. Florens & M. Mouchart, 1985. "Conditioning In Dynamic Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 6(1), pages 15-34, January.
    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.
    7. Chib, S. & Osiewalski, J. & Steel, M.F.J., 1992. "Posterior inference on the degrees of freedom parameter in multivariate-t regression models," Other publications TiSEM b3503d30-82f3-4ab4-906f-3, Tilburg University, School of Economics and Management.
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    Cited by:

    1. Jacek Osiewalski, 2011. "Bayesian Variations on the Frisch and Waugh Theme," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 3(1), pages 39-47, March.
    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.

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