Sequential classification methods
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Sequential classification methods are suggested for the case of two or more populations. First, a method for two populations with known probability densities is presented. The method is based on the likelihood ratio and Wald's method of sequential testing of simple null hypothesis against an alternative hypothesis. Two approximate methods for obtaining boundaries, in the form of inequalities for the likelihood ratios, are suggested. The classification for more populations is based similarly on simple inequalities for sequential likelihood ratios based on increasing numbers of measurements. The method is completed by the Bayes decision rule used in the case in which the entire a priori established maximal dimension of measurements is reached. Again two ways of obtaining approximate boundaries are presented. As an example for the case of two populations, the sequential classification rules for normal distributions with known mean vectors and known and unequal covariance matrices are constructed. These rules are in fact quadratic discriminant functions for the sequence of dimensions. The rest of the paper is devoted to a comparison of the methods suggested from the point of view of their conservativeness and power.