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Studentization and prediction in a multivariate normal setting

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

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.

Suggested Citation

  • Morris L. Eaton & D. A. S. Fraser, 2005. "Studentization and prediction in a multivariate normal setting," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 59(3), pages 268-276, August.
  • Handle: RePEc:bla:stanee:v:59:y:2005:i:3:p:268-276
    DOI: 10.1111/j.1467-9574.2005.00297.x
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