Sankhya: The Indian Journal of Statistics

1998, Volume 60, Series A, Pt. 3, pp. 363-382

A NEW PREDICTIVE DISTRIBUTION FOR NORMAL MULTIVARIATE LINEAR MODELS

By

MORRIS L. EATON and WILLIAM D. SUDDERTH, University of Minnesota, Minneapolis

SUMMARY. Predictive distributions are calculated in the MANOVA problem for a class of relatively invariant improper prior distributions. An invariance argument then shows that many of the predictive distributions recommended in the literature are strongly inconsistent in the sense of M.Stone. In particular, this is true of the formal Bayes prediction based on the Jeffreys prior. We introduce a new predictive distribution that is not strongly inconsistent.

AMS (1991) subject classification.62H05, 62H99, 62A05, 62A30.

Key words and phrases. Predictive inferences, improper prior distributions, strong inconsistency, invariance, multivariate linear models.

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