Separating a mixture of two normals with proportional covariances

We propose a simple affine equivariant clustering method, based on the idea of best linear classification, for samples from a mixture of two multivariate normal distributions with different mean vectors but proportional covariance matrices. To ameliorate the curse of dimensionality, a non-parametric approach to find candidates for a best linear discriminant function is presented. By using simulation studies and a real example, we show that for large samples in high dimensions, the proposed method can be a useful supplement to general-purpose multivariate outlier detection methods.