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Bayesian inference in spherical linear models: robustness and conjugate analysis

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  • Arellano-Valle, R.B.
  • del Pino, G.
  • Iglesias, P.
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    Abstract

    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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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 97 (2006)
    Issue (Month): 1 (January)
    Pages: 179-197

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    Handle: RePEc:eee:jmvana:v:97:y:2006:i:1:p:179-197

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    Related research

    Keywords: Linear regression models Elliptical and squared-radial distributions Elliptical density generator Dispersion and dispersion-location elliptical models Bayes estimator Conjugate families;

    References

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    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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    1. Osiewalski, J. & Steel, M., 1991. "Bayesian Marginal Equivalence of Elliptical Regression Models," Papers 9119, Tilburg - Center for Economic Research.
    2. Osiewalski, J. & Steel, M., 1990. "Robust Bayesian Inference In Elliptical Regression Models," Papers 9032, Tilburg - Center for Economic Research.
    3. 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.
    4. Arellano-Valle, Reinaldo B., 2001. "On some characterizations of spherical distributions," Statistics & Probability Letters, Elsevier, vol. 54(3), pages 227-232, October.
    5. Arellano-Valle, Reinaldo B. & Bolfarine, Heleno, 1995. "On some characterizations of the t-distribution," Statistics & Probability Letters, Elsevier, vol. 25(1), pages 79-85, October.
    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.
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    Cited by:
    1. Casanova, María P. & Iglesias, Pilar & Bolfarine, Heleno & Salinas, Victor H. & Peña, Alexis, 2010. "Semiparametric Bayesian measurement error modeling," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 512-524, March.
    2. Vidal, Ignacio & Arellano-Valle, Reinaldo B., 2010. "Bayesian inference for dependent elliptical measurement error models," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2587-2597, November.

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