Linear discrimination for three-level multivariate data with a separable additive mean vector and a doubly exchangeable covariance structure

In this article, we study a new linear discriminant function for three-level m-variate observations under the assumption of multivariate normality. We assume that the m-variate observations have a doubly exchangeable covariance structure consisting of three unstructured covariance matrices for three multivariate levels and a separable additive structure on the mean vector. The new discriminant function is very efficient in discriminating individuals in a small sample scenario. An iterative algorithm is proposed to calculate the maximum likelihood estimates of the unknown population parameters as closed form solutions do not exist for these unknown parameters. The new discriminant function is applied to a real data set as well as to simulated data sets. We compare our findings with other linear discriminant functions for three-level multivariate data as well as with the traditional linear discriminant function.