ML CLASSIFICATION DISTANCES AND RULES IN THE NORMAL POPULATIONS WHEN COVARIANCE MATRICES ARE UNEQUAL

抄録

Three classification rules in the discriminant problem of k normal populations having different covariance matrices are proposed. Each rule is based on a classification distance which is deduced by the likelihood procedure and defined as a distance from analogical inference of the Mahalanobis' distance. Classification rule-Z and-W for the different covariance matrices are shown to correspond to those of common covariance matrix. Classification rule-B takes into account the effect of sample size variation. The limiting distributions of these distances and associated statistics are studied. To compare these classification rules numerical examples are shown and their usefulness is discussed.