Statistical inference for bivariate two-component normal mixtures: Characterization of representative points and efficient parameter estimation

Abstract

Multivariate normal mixtures are prevalently adopted especially when sub-populations are observed in data. The representative points under mean squared error (MSE-RPs) are promising in statistical inference, but their characterization for normal mixtures has not been thoroughly investigated. The sequential number-theoretic optimization (SNTO) method shows potential advantages for estimating one-dimensional normal mixtures but encounters challenges in high-dimensional cases. Hence, initially concentrating on the mixture of bivariate two-component normal distributions, we examine the modality of bivariate location mixture density and its connection to the uniqueness of MSE-RPs from the perspective of projection. We propose a new parameter estimation method in order to overcome the challenges of the SNTO through the projection pursuit method and a reparametrization technique for covariance matrices.