Multivariate mixture data analysis presents numerous challenges and constitutes a vital area of interest in the fields of statistics and data science. Research into multivariate mixture structures holds relevance across diverse application domains and plays a pivotal role in the advancement of artificial intelligence and machine learning. In this paper, we focus on nonparametric estimation techniques for multivariate mixture data. Specifically, we assume a known number of subpopulations and propose a binomial likelihood method, along with an efficient numerical algorithm, to estimate the mixing proportions and cumulative distribution functions of these subpopulations without relying on parametric assumptions. Through extensive numerical experiments, we demonstrate three key advantages of our approach: (1) Our method eliminates the need for tuning parameters. (2) It does not require the assumption of continuous component density functions. (3) Our method consistently delivers stable performance. Under mild regularity conditions, we provide theoretical proofs for the L_2 convergence and uniform convergence of our estimators. To illustrate the practical performance of our method, we include a real-data example.
