Generalization of the Mahalanobis distance in the mixed case
In discrimination, as in many multivariate techniques, computation of a distance between two populations is often useful. For example, in taxonomy one can be interested not only in discriminating between two populations but in having an idea of how far apart the populations are. Mahalanobis' \(\Delta^ 2\) has become the standard measure of distance when the observations are quantitative and Hotelling derived its distribution for normal populations. The aim of this article is to adapt these results to the case where the observed characteristics are a mixture of quantitative and qualitative variables. In the first section a generalisation of the Mahalanobis distance is given. Then, in the second section, its asymptotic probability distribution is obtained. In the third section, the rate of convergence and the power of the test are compared through simulation. An example is presented in the last section.
mixture of discrete and continuous variables
mixture of quantitative and qualitative variables
generalisation of the Mahalanobis distance
scientific article; zbMATH DE number 769842