Combinatoric classification of multivariate normal observation vectors

Abstract

The discrimination problem consisting of classifying an nxl observation vector as coming from one of two multivariate normal distributions which differ both in their mean vectors and covariance matrices is considered. A search for the procedure which minimizes the expected cost of misclassification is conducted within the class of procedures based upon a certain combination of n independent univariate discriminations. An efficient search of this class of procedures is made by employing an algorithm of the implicit enumeration type used in integer programming. In the case of known population parameters, the independent discriminant functions and exact probabilities of misclassification are found. When the parameters are unknown, estimates are introduced for the coefficients of each univariate discriminant function and for the probabilities of misclassification. A jackknife procedure is introduced in order to improve the estimation process. The method is applied to the problem classifying a set of male twins as to whether they are monozygotic or dizygotic.