Statistical Inference For Mixture Models With Skew-t-normal Data

It obtains rapid development is a major thrust of big data for economy,science and technology.Every little thing in daily life can have a connection with big data through the network,such as:all kinds of statistics.In order to facilitate analysis,people usually put them idealized and as a simple and common distributed,which people have access to the data is multifarious,such as normal distribution and t distribution.Putting all the data together,ignoring the unique characteristics and will mislead the results of the analysis;which outstanding hybrid data have the great importance in the statistical analysis.In fact,these data and has certain characteristics of multifarious mixture.In order to better describe the characteristics of the data itself,researchers often classify statistics to analyze data,namely the data clustering analysis.Clustering analysis is the overall data classified according to different indicators or features,and further analysis the data,which reduces a lot of work in the study of large data.People have access to the data is not strictly obey the normal distribution,t distribution or skewness normal distribution in the field of economy,but they obey has obvious deflection fat-tailed distribution.In comparison,Skew-t-normal distribution can better depict that has obvious the characteristics of peak and fat tail data.It's widely known that the classical linear regression model is no longer widely used significance,because there are a large amounts of heteroscedastic data in economics,medicine,environmental science and engineering technology.Which makes it is necessary to model the variance,so statistical scholars proposed joint mean and variance model and which is one of the most important research tools to process heteroscedasticity.In order to solve the numerous and complicated data in the life,the researchers proposed mixture regression models,which main research contains two or more than two children of mixed data clustering.The model make the mixture data get a better fitting.Besides,considering the universality and practicability of the model,the scholars study the linear model is extended to nonlinear model in different areas and different models.In this paper,based on mixture skew-t-normal data,heterogeneous population,heteroscedasticity,linear models and non-linear models,we investigate the maximum likelihood estimate for unknown parameters based on Expectation Maximization(EM)algorithm and Newton-Raphson algorithm with skew-t-normal distribution.The main content includes the following sections:Firstly,Under the precondition of mixture skew-t-normal data,and established linear model for location parameters.We propose mixture linear model with skew-t-normal data.Then we investigate the maximum likelihood estimate for unknown parameters based on Expectation Maximization(EM)algorithm and give the formulas which the Expectation Maximization(EM)algorithm need.Furthermore,we make some simulations to show that the proposed procedure works satisfactorily.Secondly,based on mixture skew-t-normal data,we not only consider the location parameters modeling but also considered the scale parameter modeling,and make them link together.we proposed the linear regression models and the linear for joint location and scale models with mixture skew-t-normal distribution data in this part and investigated the maximum likelihood estimate for unknown parameters based on the Expectation Maximization(EM)algorithm.Furthermore,by Monte Carlo simulation research and analysis human body index(BMI)data,further proves the universality of model and the feasibility of the method.Finally,On the basis of above research,realizing the importance of skewness parameters,added to the parametric modeling of skewness.Considering the general model,the linear model is extended to nonlinear model.On the basis of the third part,we made a nonlinear model for the skewness parameter and proposed mixture of nonlinear for joint location,scale and skewness models with mixture skew normal distribution data in this part.Then we investigated the maximum likelihood estimate for unknown parameters based on Expectation Maximization(EM)algorithm and Newton-Raphson algorithm.Lastly we make some simulations to show that the proposed procedure works satisfactorily.