On confidence regions in canonical variate analysis

Abstract

It is argued that confidence circles as traditionally drawn on canonical variate diagrams are incorrect, because no allowance is made in their construction for the sampling variability of the canonical variate axes. A series of approximations is employed to obtain tractable expressions for the correct regions. Despite the rather broad approximations involved, empirical assessment via bootstrapping shows the new regions to have much more accurate probability content than the traditional circles. An illustrative example highlights the differences between the two types of region.