ASYMPTOTIC-EXPANSION OF THE MISCLASSIFICATION PROBABILITIES OF D-CRITERIA AND A-CRITERIA FOR DISCRIMINATION FROM 2 HIGH-DIMENSIONAL POPULATIONS USING THE THEORY OF LARGE DIMENSIONAL RANDOM MATRICES

In this paper some ideas on experimental designs are used in discriminant analysis. By considering the populations as groups, one may classify a new observation by minimizing a suitable norm of the within groups sum of squares and cross products matrix after assigning it to each group. The classification based on the D-criterion is identical to that based on the maximum likelihood ratio criterion. For a high dimensional setting with measurement space (p) nearly equal to the total sample size (n), the A-criterion performs better than the D-criterion. Approximate misclassification error probabilities were derived using Edgeworth expansions and it is shown these agree closely with simulated results. © 1993 Academic Press Inc.