Statistical Inference and Algorithm Design of Mixture Model with Change Point

This paper studies the statistical inference and algorithm design problems in the mixture model with change point. For multi-classified mixture data with change point, this paper designs an improved EM algorithm based on the maximum likelihood estimation of parameters, and proves the large sample nature of the change point estimator and the mixture parameter estimator. In order to verify the effectiveness of the method, we conducted some simulation experiments. The results show that the EM algorithm that does not consider the change point has a poor estimate on the classification result, and even loses some categories; Our improved EM algorithm can accurately locate the location of the change point, and at the same time obtain accurate estimates for the corresponding parameters of each category.