Statistical Inference For Joint Mean And Dispersion Models With Mixture Data

In statistical analysis, the classical regression model can no longer be used to depict the mixed data that is more and more close to reality. As to the mixture data which numerously exist in real life, the clustering analysis method of multivariate statistical analysis is one of the important statistical tools to analysis the mixture data. In order to deeply analysis the relations between the mixed data, many statistical scholars researched and then proposed mixture regression model. Because of the promoting and application of mixed regression model, it becomes more accurate and practical to analyze two or more than two sub clustering mixed data. And the existence of a large number of mixted heteroscedasticity data has great influence to the reality, so we need to explore the sources of variance, understand the factors that influence the fluctuation of variance and it is neccessary to make models of variance, fully understand the sources of variance, and control the variance. So this article systematically studied and proposed mixture joint mean and dispersion models to analysis and deal with the mixture heteroscedasticity data. The concrete content includes the following several parts:First, in this paper, we mainly use the mixed regression model and the double generalized linear models. As statistical methods, the mixed regression model can be used to research the two or more than two sub clustering mixed data. This model has very high practical value in insurance, biology, medicine, finance and other fields; And double generalized linear models can be applied in more applicable scope than the general linear model, the advantage of this model is that it not only model the simulated mean value but also the unequal variance, so we can effectively understand the information of variance sources, and timely control of the variance of non homogeneity.Second, we established a generalized linear joint mean and dispersion models of specific inverse Gaussian and lognormal distribution in the mixed data. And also, we make full use of the EM algorithm to estimated the model parameters. Finally, through the Carlo Monte simulation, it is concluded that the parameter method is effective and feasible.Third, we established generalized linear joint mean and dispersion models in the mixed tweedie distribution, estimate the parameters maximum likelihood by the method of extended quasi-likelihood and pseudo-likelihood. From the simulation and case study, we can see that the two estimation methods are effective, practical and accurate.