Statistical Inference And Algorithm Design Of Mixture Parameter Model With Change Point

The statistical inference and calculation of parameters on the mixture model is one of the hot issues in the field of statistics research.At the same time,the related theories for change point detection and estimation are also widely used in the fields of statistics,biology and econometrics.Testing and estimating the existing change points in mixture data has important practical significance for us to understand the nature of things change and make relevant decisions.This paper studies the statistical inference and algorithm design of the parameters in the mixture model with change point,mainly considering two different situations: the mixture local model and the mixture linear model.For the mixture local model,constructing the test statistics through hypothesis testing,and discussing their limit properties under the null hypothesis and alternative hypothesis separately to detect the existence of change points;for multi-class mixture data with change points,this paper designs an improved EM algorithm,which can estimate the change point and the mixture parameters at the same time.Furthermore,we prove the consistency of the change point estimator and the mixture parameter estimators.In order to verify the effectiveness of the method,we carry out two different component-settings numerical simulation experiments.The results show that the EM algorithm that without considering the change point has a poor estimation for the classification results,regardless of the two-component or multi-component situation,and even loses some categories;The improved EM algorithm can accurately locate the location of the change point and at the same time obtain accurate estimations for the corresponding parameters of each category.On the basis of the mixture local model,this paper also considers the problem of change points in the mixture linear model.Similarly,the improved EM algorithm can be used to estimate the change point position and the mixture parameters at the same time,and the large sample nature of the parameter estimator is proved.Finally,by setting up numerical simulation experiments with different data volumes,we can obtain the parameter estimators and standard error trends under the two methods to verify the correctness of the theory.The results show that our improved EM algorithm can obtain more accurate parameter estimators,and the standard error of the estimators show a downward trend as the amount of data increases,that is,the improved method is still very effective in this case.