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Posterior moments of scale parameters in elliptical regression models

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

Abstract

In the general multivariate elliptical class of data densities we define a scalar precision parameter r through a normalization of the scale matrix V. Using the improper prior on r which preserves the results under Normality for all other parameters and prediction, we consider the posterior moments of r. For the subclass of scale mixtures of Normals we derive the Bayesian counterpart to a sampling theory result concerning uniformly minimum variance unbiased estimation of 7. 2 • If the sampling variance exists, we single out the common variance factor i' as the scalar multiplying V in this sampling variance. Moments of i' are examined for various elliptical subclasses and a sampling theory result regarding its unbiased estimation is mirrored.

Suggested Citation

  • Osiewalski, Jacek & Steel, Mark F.J., 1992. "Posterior moments of scale parameters in elliptical regression models," UC3M Working papers. Economics 10879, Universidad Carlos III de Madrid. Departamento de Economía.
    • Handle: RePEc:cte:werepe:10879
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    References listed on IDEAS

    as
    1. Chib, S. & Osiewalski, J. & Steel, M.F.J., 1990. "Posterior inference on the degrees of freedom parameter in multivariate-t regression models," Other publications TiSEM 9d607045-c51b-40b4-9aa3-d, Tilburg University, School of Economics and Management.
    2. Chib, Siddharta & Osiewalski, Jacek & Steel, Mark F. J., 1991. "Posterior inference on the degrees of freedom parameter in multivariate-t regression models," Economics Letters, Elsevier, vol. 37(4), pages 391-397, December.
    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. Osiewalski, Jacek & Steel, Mark F.J., 1991. "Robust bayesian inference in empirical regression models," UC3M Working papers. Economics 2814, Universidad Carlos III de Madrid. Departamento de Economía.
    6. Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
    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.
    8. 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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