On some parametric, nonparametric and semiparametric discrimination rules

We consider two populations (groups) P-1 and P-2 having continuous k-variate probability densities of elliptical form. Our goal is to allocate a new observation x is an element of R-k to one of these two groups. We do not know exact forms of underlying distributions but they can be estimated using training samples which are random samples from these populations. If we assume that both distributions are multinormal, the training samples yield estimates of the mean vectors and covariance matrices, and Fisher's linear and quadratic discrimination rules are obtained. If the population models are unknown, alternative estimates of location and scatter as well as estimates of distributional forms are needed; in this paper the multivariate density estimates and resulting rules are parametric, semiparametric and nonparametric. We consider six different methods, including classical linear and quadratic discriminant analysis, for discriminating between two populations and compare these methods in a small simulation study.