Research On Bias Estimation Of Semiparametric Regression Model

In recent years, the research for linear statistical models and the discussion of the parameter estimation problem is becoming more and more mature. Many studies have been widely used in practice. The estimation of semi-parametric regression model has gradually developed a kind of new research on parameters of statistical model since the 1980s, which can be divided into two parts:one part is the linear regression, the other part is the unknown quantity observation factors. Therefore, it can overcome the limitations of parameter model to express the objective model. It becomes closer to the true about describing practical problems. It also has more theoretical value and practical significance to do some corresponding research in the estimation of semi-parametric regression model.The mainly research of this article is discussing with the semi-parametric regression model and its categories biased estimate, the following work has been done:The first part’s theoretical research of this article is to propose the principal component estimate based with the semi-parametric regression model, and then I will research about its theoretical properties of corresponding, and prove, if it satisfy the corresponding conditions, that it is superior to least squares estimate under mean square error(MSE).The second part’s theoretical research of this article is to accord the researches of the linear regression model to propose a semi-parametric regression model of principal component estimate ridge type, and then I will research about its theoretical properties of corresponding, and prove, if it satisfy the corresponding conditions, that it is superior to least squares estimate under MSE.The third part’s theoretical research of this article is to discuss in the sense of MSE, if it satisfy the corresponding conditions, that the principal components regression ridge estimator for the parametric component is superior to the single principal components estimation and the single ridge method estimation.The fourth part’s theoretical research of this article is to append a certain constraint b= Aβ to the parameter. Then I will propose a principal components regression ridge estimator for the parametric component of semi-parametric regression model under the constraint condition, and prove, if it satisfy the corresponding conditions, that in the sense of MSE, When it has the constraint condition, the principal components estimator is superior to the ordinary least squares estimation, the principal components regression ridge estimator for the parametric component is better than the ridge estimation.The fifth part’s theoretical research of this article is to append a stochastic constraint b= Aβ+η to the parameter. Then I will propose a principal components regression ridge estimator for the parametric component of semi-parametric regression model under the stochastic condition, and discuss with their some related properties.The sixth part’s theoretical research of this article is to study the theory on the above and use R software to make the relevant Monet Carlo simulation.