Parameter Estimation And Order Selection In Finite Mixture Models

Under the circumstances of big data age,the large and complex data set always comes from different species or groups.Finite mixture models form a flexible tool to deal with the heterogeneity.As the top priority of application,it is a significant step to study the mathematical problems.In this thesis,we investigate two problems in finite mixture models.One is the problem of parameter estimation given the number of components of the model.Another one is to do order selection,that is,to determine the number of components.As to the first problem,we propose three modified EM algorithms for parameter estimation in finite mixture models.The proposed methods replace the mixing proportions with other estimates while calculating the conditional expectations for the hidden labels given observations and the current estimates for parameters in the E step.We also discuss the convergence properties of the new procedures.Simulation studies show that the new acceleration methods perform much better than the classical EM algorithm in convergence rate and estimation accuracy.A real-data example is examined to illustrate their performance.Regarding the second problem,a penalized likelihood method with MCP penalty is proposed,called MMCP.To be specific,based on likelihood function,the pro-posed method introduces two penalty functions on the mixing proportions and the distance between component parameters.The new method can do order selection and parameter estimation simultaneously.Numerical studies show that the new method perform better than MSCAD.