Discriminant Analysis of Normal Populations with Different Covariation Matrices

The author examines a hypothesis regarding the structure of two normal populations and the links between this hypothesis and a procedure that makes it possible, as the paper, shows, to evaluate the parameters of the hypothesis. It is shown that if the populations are represented by large samples, the separating surface constructed in accordance with the hypothesis will possess smaller sampling errors than in the case of the widely employed hypothesis $\mathbf M_1\ne\mathbf M_2$, $\mathbf{\Sigma}_1\ne\mathbf{\Sigma}_2$.