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 InfoPaper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 1997-104.
Date of creation: 1997
Date of revision:
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Web page: http://center.uvt.nl
Behrens-Fisher problem; Fieller-Creasy problem; Gibbs sampling; Jeffreys' prior; location-scale model; posterior existence; product of means; scale mixtures of normals; skewness;
Other versions of this item:
- Carmen Fernández & Mark Steel, 1998. "Reference priors for non-Normal two-sample problems," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 7(1), pages 179-205, June.
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- Steel, M.F.J., 1991.
"Bayesian Inference in Time Series,"
9153, Tilburg - 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.
- 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.
- 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.
- Geweke, J, 1993. "Bayesian Treatment of the Independent Student- t Linear Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages S19-40, Suppl. De.
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