ON THE NONCENTRAL DISTRIBUTION OF A RANDOM MATRIX USEFUL IN CLASSIFICATION THEORY

Abstract

SummaryTo prove the optimality properties of the maximum likelihood (and also minimum distance) discriminant rule Rogers (1980, p. 98) embeds the maximum likelihood discriminant function in a Cauchy‐Schwartz inequality. This embedding procedure of Rogers (1980) may be used to derive a new distribution for Anderson's (1958) classification statistic.