Canonical mean projections and confidence regions in canonical variate analysis

Abstract

In developing confidence regions for canonical mean variates, Krzanowski (1989) made use of approximate asymptotic variances and covariances of the elements of the canonical variate coefficient vectors. This procedure is improved upon by the use of the asymptotically correct variances and covariances. However, comparisons of the confidence regions, with and without this improvement, reveal that both perform inadequately if the latent roots corresponding to the canonical variates involved are not well separated. An alternative method based on confidence regions for a canonical mean projection is proposed. The performances of these confidence regions are investigated in a simulation and the method is illustrated by a numerical example.