Reference priors for non-Normal two-sample problems
AbstractThe reference prior algorithm (Berger and Bernardo, 1992) is applied to locationscale models with any regular sampling density. A number of two-sample problems is analyzed in this general context, extending the di erence, ratio and product of Normal means problems outside Normality, while explicitly considering possibly di erent sizes for each sample. Since the reference prior turns out to be improper in all cases, we examine existence of the resulting posterior distribution and its moments under sampling from scale mixtures of Normals. In the context of an empirical example, it is shown that a reference posterior analysis is numerically feasible and can display some sensitivity to the actual sampling distributions. This illustrates the practical importance of questioning the Normality assumption.
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Bibliographic InfoArticle provided by Springer in its journal Test.
Volume (Year): 7 (1998)
Issue (Month): 1 (June)
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Web page: http://www.springerlink.com/link.asp?id=120411
Other versions of this item:
- Fernández, C. & Steel, M.F.J., 1997. "Reference Priors For Non-Normal Two-Sample Problems," Discussion Paper 1997-104, Tilburg University, Center for Economic Research.
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- S. Ghosal, 1997. "Reference priors in multiparameter nonregular cases," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 6(1), pages 159-186, June.
- Steel, M.F.J., 1991.
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- Fernández, C. & Steel, M.F.J., 1996. "On Bayesian Modelling of Fat Tails and Skewness," Discussion Paper 1996-58, Tilburg University, Center for Economic Research.
- D. Stephens & A. Smith, 1992. "Sampling-resampling techniques for the computation of posterior densities in normal means problems," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 1(1), pages 1-18, December.
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