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Reference priors for non-Normal two-sample problems

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  • Carmen Fernández
  • Mark Steel

Abstract

The 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 dierence, ratio and product of Normal means problems outside Normality, while explicitly considering possibly dierent 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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Suggested Citation

  • 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;Sociedad de Estadística e Investigación Operativa, vol. 7(1), pages 179-205, June.
    • Handle: RePEc:spr:testjl:v:7:y:1998:i:1:p:179-205
    DOI: 10.1007/BF02565109
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    References listed on IDEAS

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    1. 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;Sociedad de Estadística e Investigación Operativa, vol. 1(1), pages 1-18, December.
    2. Geweke, J, 1993. "Bayesian Treatment of the Independent Student- t Linear Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages 19-40, Suppl. De.
    3. Fernández, C. & Steel, M.F.J., 1996. "On Bayesian Modelling of Fat Tails and Skewness," Other publications TiSEM 0991c197-c9e8-4904-8119-3, Tilburg University, School of Economics and Management.
    4. S. Ghosal, 1997. "Reference priors in multiparameter nonregular cases," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 6(1), pages 159-186, June.
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