A nonparametric estimation method for the multivariate mixture models

In this paper we study the estimation of the mixing proportions and component density functions for a nonparametric multivariate mixture model that satisfies the condition of identifiability. We propose a new estimation method which combines the advantages of the matrix simultaneous diagonalization method and the basis method. The consistency of the estimator is proved and its convergence rate is derived. Simulations are conducted to evaluate the performance of the proposed method. The method is also applied to the US communities and crime data set. Numerical simulations and real data analysis show the good performance with low computational cost of the new method in the estimation for the multivariate mixture models.