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 |
|
|