Maximum Binomial Likelihood Method for Multivariate Mixture Data
提出一种无需参数假设的二项式似然方法，用于估计多元混合数据中各子群的混合比例和累积分布函数，并通过数值实验证明其无需调参、不要求连续密度且性能稳定。
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: (Citation1) Our method eliminates the need for tuning parameters. (Citation2) It does not require the assumption of continuous component density functions. (Citation3) Our method consistently delivers stable performance. Under mild regularity conditions, we provide theoretical proofs for the asymptotical properties of our estimators. To illustrate the practical performance of our method, we include a real-data example.