Study On Semiparametric Model

A semiparametric model has been an important statistics model since 1980s, this kind of model includes not only a parametric component, but also a nonparametric component. So it has the advantages of the parametric model and the nonparametric model. It has the more implements and stronger explanations than the pure parametric or nonparametric model.In this paper, we mostly study the penalized least squares method and the kernel smoothing method of the semiparametric model. The discussed contents include the methods of getting the estimators, the statistical properties of the estimators, the asymptotic properties of the estimators, the compare between the estimator got from the penalized least squares method or the kernel smoothing method and least squares method under the principle of MSE, the stimulation of the data by using the software of Matlab to affirm the effect of the estimator.The mostly studied contents in this paper are as follows.1) Discussed the estimate methods of semiparametric model, mostly discussed the method of the penalized least squares method and the kernel smoothing method. Analyzed the statistical properties of these two methods. Special in asymptotic properties in situation of big samples. Under the criteria of MSE, compared the penalized least squares method and the kernel smoothing method with the least squares method. Proved that the penalized least squares method and the kernel smoothing method is better than the least squares method.2) Studied the regular matrix and the smooth factor, gave some choice method of them. Studied the choices of kernel function's bandwidth, gives some data-based criteria.3) At last we give stimulation by software of Matlab to show the effect of the estimator. Proved the effect of the penalized least squares method and the kernel smoothing method is better than the least squares method.