A parametric method for dividing a heterogeneous multivariate population into components is proposed. The method includes the following operations: (1) The mixed population is divided into two parts by a linear discriminant function with arbitrary coefficients; (2) The parameters of both parts are evaluated and then a new linear discriminant function is built, determining the second division. This new division is shown to be better (i.e., to provide a less misclassification probability) than the initial one; (3) The change in direction of the dividing hyperplane found in this way is extrapolated until the best division (in the above sense) in this extrapolation course is achieved; (4) A discriminant correction is carried out, determining a new course of extrapolation, and so on. This process may be controlled by analysing the one-dimensional distribution obtained by mapping the multivariate distribution into the line normal to the dividing hyperplane. Division into several components is made by successive dichotomies. Some problems concerning the use of finite samples are discussed.
