A decision rule for dimension in the context of Manova

Abstract

An ad hoc rule is proposed to determine the dimension of the space generated by the mean vectors centered at the origin. Under normality, the proposed ad hoc rule is close to being Bayes for a prior which seems to distribute the total mass in a reasonable way. The ad hoc rule is then slightly modified to incorporate some of the finer features of the Bayes rule without losing good frequentist features. Simulation studies show that the rule nearly attains the Bayes risk and so is nearly admissible. It has other attractive frequentist features.