Studentization and prediction in a multivariate normal setting

Morris L. Eaton and D. A. S. Fraser

Statistica Neerlandica, 2005, vol. 59, issue 3, 268-276

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.

Date: 2005
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https://doi.org/10.1111/j.1467-9574.2005.00297.x

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