Statistical Inference For Reproductive Dispersion Models With Mixture Data

Reproductive dispersion family is more widespread family than the exponential family,so it is more applicable.Normal distribution,Poisson distribution,Gamma distribution,I-type extreme distribution and double exponential distribution are special cases of the distribution.In the analysis and research of complex data and longitudinal data,the mixture regression model is one of the useful statistical analysis tools.Based on the mean model with heteroscedastic data,it is necessary to model the variance in order to effectively control the variance.Mixture of regression for joint position and dispersion models based on the reproductive dispersion family are formed.Then,mixture of expert regression for joint position and dispersion models based on the reproductive dispersion family are formed by the mixing ratio modeling.The models are widely useful,so the study of the models are one of the hot topics in statistics.Firstly,assuming that the number of components of model is known based on the reproductive dispersion family,and the position parameters are modeled.Using EM algorithm,the maximum likelihood estimations of unknown parameters are obtained in the model.Simulation studies and a real example analysis illustrate that the model and method is effective and useful.Secondly,position parameters and dispersion parameters are modeled,and the identifiableness of the model is proved.Using EM algorithm,the maximum likelihood estimations of unknown parameters are obtained in the model.Simulation studies and a real example analysis illustrate that the model and method is effective and useful.Finally,based on the above studies,to understand the factors that affect the mixed proportion,a mixture of expert model is introduced,logistic regression is used to model the proportional parameters.Using EM and MM algorithm,the maximum likelihood estimations of unknown parameters are obtained in the model.Simulation studies and a real example illustrate that the model and method is effective and useful.In summary,a series of new results are obtained in the context of reproductive dispersion models,which extends and develops the existed work and results.These new results are not only feasible in theory,but also useful in practice.This thesis illustrates the model and method is effective and useful through simulation studies and example analysis.