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Reference Priors For Non-Normal Two-Sample Problems

Fernández,C.
; 
Steel,M.F.J.
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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Pagination: 21
Date
1997
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Publisher
Econometrics
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Tilburg University Research Output Collection
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104.pdf
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Keywords
Behrens-Fisher problem, Fieller-Creasy problem, Gibbs sampling, Jeffreys' prior, location-scale model, posterior existence, product of means, scale mixtures of normals, skewness
Citation
Fernández, C & Steel, M F J 1997 'Reference Priors For Non-Normal Two-Sample Problems' CentER Discussion Paper, vol. 1997-104, Econometrics, Tilburg.
URI
https://hdl.handle.net/20.500.14602/26429
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