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.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 97 (2006)
Issue (Month): 1 (January)
|Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description|
|Order Information:|| Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional|
References listed on IDEAS
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.:
- 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.
- OSIEWALSKI, Jacek, .
"Robust Bayesian inference in elliptical regression models,"
CORE Discussion Papers RP
-1047, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Osiewalski, Jacek & Steel, Mark F. J., 1993. "Robust bayesian inference in elliptical regression models," Journal of Econometrics, Elsevier, vol. 57(1-3), pages 345-363.
- Osiewalski, J. & Steel, M., 1990. "Robust Bayesian Inference In Elliptical Regression Models," Papers 9032, Tilburg - Center for Economic Research.
- Osiewalski, J. & Steel, M.F.J., 1990. "Robust Bayesian inference in elliptical regression models," Discussion Paper 1990-32, Tilburg University, Center for Economic Research.
- 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.
- Osiewalski, J. & Steel, M., 1991.
"Bayesian Marginal Equivalence of Elliptical Regression Models,"
9119, Tilburg - Center for Economic Research.
- Osiewalski, Jacek & Steel, Mark F. J., 1993. "Bayesian marginal equivalence of elliptical regression models," Journal of Econometrics, Elsevier, vol. 59(3), pages 391-403, October.
- Osiewalski, J. & Steel, M.F.J., 1991. "Bayesian marginal equivalence of elliptical regression models," Discussion Paper 1991-19, Tilburg University, Center for Economic Research.
- Arellano-Valle, Reinaldo B., 2001. "On some characterizations of spherical distributions," Statistics & Probability Letters, Elsevier, vol. 54(3), pages 227-232, October.
- 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.
When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:97:y:2006:i:1:p:179-197. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.