Studentization and Prediction in a Multivariate Normal Setting
نویسنده
چکیده
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 that does not have a parameter free distribution – that is, is not an ancillary statistic. In contrast, a predictive distribution derived by a structural argument is based on a pivot with a fixed 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.
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