A Study On Some Regression Models

Regression analysis is a kind of classical statistical models, and its conventional method for parameter estimation is ordinary least squares. In rescent years, regression analysis has been greatly developed and a great deal of new models and parameter estimation methods have been proposed. In this paper, we try to give a theoretical analysis and numerical simulations for some of these models and approaches in order to provide beneficial reference to theoretic researches and practical applications.Our main research works are as follows:1. On theoretical analysis and simulations of Guassian mixture regression model. We first introduce Guassian mixture model and its parameter estimation methods. Then the Guassian mixture regression model and correlative theoretic results are introduced. By comparing with other conventional regression methods, the estimstion results in numerical simulations are analysed and evaluated on the basis of model accuracy and robustness.2. On theoretical analysis and simulations of mixture regression model. We introduce the basic theories of mixture regression model and discuss some present parameter estimation methods for this model. A novel Markov chain Monte Carlo (MCMC) method and its implementation strategy are proposed for estimating the parameters in mixture regression model. The effectiveness of the proposed MCMC method is illustrated and compared by the EM algorithm in experimental simulations.3. On theoretical analysis and simulations of multilevel regression model. The basic theories of multilevel regression models are introduced, including the several types of models and the corresponding estimation methods. By comparing with present regression methods, the multilevel regression model is analysed and evaluated from the real data in experiments.