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Studentization and prediction in a multivariate normal setting
Authors:Morris L Eaton  D A S Fraser †
Institution:University of Minnesota, School of Statistics, 313 Ford Hall, 224 Church Street S.E., Minneapolis, MN 55455 USA; University of Toronto, Department of Statistics, 100 St. George Street, Toronto, Canada, M5S 3G3
Abstract:In a simple multivariate normal prediction setting, derivation of a predictive distribution can flow from formal Bayes arguments as well as pivoting arguments. We look at two special cases and show that the classical invariant predictive distribution is based on a pivot whose sampling distribution depends on the parameter – that is, the pivot is not an ancillary statistic. In contrast, a predictive distribution derived by a structural argument is based on a pivot with a parameter free distribution (an ancillary statistic). The classical procedure is formal Bayes for the Jeffreys prior. Our results show that this procedure does not have a structural or fiducial interpretation.
Keywords:pivotal quantities  ancillarity  formal Bayes predictive distribution
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