Discriminant analysis in small and large dimensions

In this article we study the distributional properties of the linear discriminant function under the assumption of the normality by comparing two groups with the same covariance matrix but di erent mean vectors. A stochastic representation of the discriminant function coefficient is derived which is then used to establish the asymptotic distribution under the high-dimensional asymptotic regime. Moreover, we investigate the classi cation analysis based on the discriminant function in both small and large dimensions. In the numerical study, a good nite-sample perfor- mance of the derived large-dimensional asymptotic distributions is documented.