Bayesian inference in spherical linear models: robustness and conjugate analysis
The early work of Zellner on the multivariate Student-t linear model has been extended to Bayesian inference for linear models with dependent non-normal error terms, particularly through various papers by Osiewalski, Steel and coworkers. This article provides a full Bayesian analysis for a spherical linear model. The density generator of the spherical distribution is here allowed to depend both on the precision parameter [phi] and on the regression coefficients [beta]. Another distinctive aspect of this paper is that proper priors for the precision parameter are discussed. The normal-chi-squared family of prior distributions is extended to a new class, which allows the posterior analysis to be carried out analytically. On the other hand, a direct joint modelling of the data vector and of the parameters leads to conjugate distributions for the regression and the precision parameters, both individually and jointly. It is shown that some model specifications lead to Bayes estimators that do not depend on the choice of the density generator, in agreement with previous results obtained in the literature under different assumptions. Finally, the distribution theory developed to tackle the main problem is useful on its own right.
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Volume (Year): 97 (2006)
Issue (Month): 1 (January)
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References listed on IDEAS
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- Arellano-Valle, Reinaldo B., 2001. "On some characterizations of spherical distributions," Statistics & Probability Letters, Elsevier, vol. 54(3), pages 227-232, October.
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- Osiewalski, J. & Steel, M.F.J., 1991. "Bayesian marginal equivalence of elliptical regression models," Discussion Paper 1991-19, Tilburg University, Center for Economic Research.
- Steel, Mark F.J. & Osiewalski, Jacek, 1992. "Bayesian marginal equivalence of elliptical regression models," UC3M Working papers. Economics 10950, Universidad Carlos III de Madrid. Departamento de Economía.
- Ng, Vee Ming, 2002. "Robust Bayesian Inference for Seemingly Unrelated Regressions with Elliptical Errors," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 409-414, November.
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