Asymptotic Expansion of the Misclassification Probabilities of D- and A-Criteria for Discrimination from Two High Dimensional Populations Using the Theory of Large Dimensional Random Matrices

H. Saranadasa

Journal of Multivariate Analysis, 1993, vol. 46, issue 1, 154-174

Abstract: 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.

Date: 1993
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