Semi-parametric Regression Model Estimation Methods And Simulation Analysis

Semiparametric regression model, also called as partial linear regression model, first introduced by Engle et al (1986) to analyze the relationship between temperature and electric demand, is an important statistic model since 1980's.In many applications of regression analysis, because of the unavoidable system errors, the independent variables may not be observed directly, but with some errors instead. However, because of the system error problem, the ordinary least square method is inefficient. So to research the semiparametric regression models is more challenging and practical than the ordinary regression models. In this paper, we introduce two pattern models of semiparametric regression models: linear semiparametric regression model and nonlinear semiparametric regression model. We also investigate the ordinary estimation methods for semiparametric regression models (Penalized least square estimate, Kernel smoothing estimate, Quasi likelihood estimate, Quasi observation approach) and obtain some satisfactory results. Now let us generally introduce our works as follows:One of the main results of the paper is firstly introduced the quasi likelihood estimation to estimate semiparametric regression models. We apply the method to linear semiparametric regression model and nonlinear semiparametric regression model. Quasi likelihood method overcomes the fault of maximum likelihood which depends on the normal distribution and the result usually will be better than the penalized least square.The second result is that we combine the semiparametric regression with the traditional approach of geodesy. It is suggested that the prior information on the semiparameters should be transformed into quasi observations. We apply quasi observation approach to estimate the semiparameters and extend the approach to estimate the nonlinear semiparametric regression models. It is worth to pay great attention to that the approach overcome the fault of traditional semiparametric estimation which is relative abstract. The third result is that we get the several methods of semiparametric regression estimation together. We also give the detailed description of the procedure and their merits and faults.