Statistical Inference Of Mixture For Joint Models

In real life,there are a large number of heterogeneous population data except homogeneous population data.For these data,mixture regression model is one of the important statistical analysis tools,and has been widely used in biology,medicine,economy,finance,environmental protection,industrial design and other fields.Mixture of expert regression model(MoE)builds proportion of mixture model on the basis of mixture regression model,and classifies,clusters and analyzes heterogeneous population data.Variable selection is an important part of statistical analysis and statistical inference,and it is also a hot topic of current research.For the mixture regression model,there are more researches on the parameter estimation instead of variable selection.Therefore,aiming at the problem of variable selection in mixture regression model,this paper systematically introduces its research overview and latest progress,and points out the problems to be further studied.The work done in this paper is as follows:Firstly,based on heterogeneous population,mixture of joint mean and variance expert regression model are proposed.In addition,MM algorithm and EM algorithm will also be used in this paper to get the estimated values of the parameters.The method to verify the validity of the model is Monte Carlo simulation experiment.The effectiveness and practicability of the proposed method are illustrated by real data.Then,the above model will be further extended,that is t-type mixture double generalized linear expert regression model.The parameters estimation will also be completed by EM algorithm.The effectiveness and practicability of the proposed method are illustrated by Monte Carlo simulation experiments.Finally,the penalty likelihood function method is used to select important variables of the mixture of joint mean and variance model.The penalty likelihood function is integrated with the likelihood function by the three different penalty functions,and the tuning parameters of mean model and variance model are selected by BIC criterion.The specific calculation process of variable selection is obtained by iteration algorithm.The simulation results further verify the feasibility of the proposed variable selection method.