The Study Of Asymptotic Properties Of Estimators In Heteroscedastic Partially Linear Regression Model

Regression analysis is an important method of statistical inference. In practical application, it become one of the statistical methods which is the most closely that theory with practice, and it is an important tool that seeking relationships between analysising data and processing data. In theory, the method of dealing with the semiparametric model is blend of regression method and nonparametric method which has developed in recent years. But it is not the simple superposition of these two kinds of method. In practical problems, the semiparametric regression model is more close to real situation and it can make full use of the information that provide in the data. Therefore we consider the semiparametric regression model instead of a single regression model is more meaningful.This article is study of the asymptotic properties of estimators in heteroscedastic partially linear regression model which is based on the existing research. Firstly, studies the heteroscedastic partially linear regression model under martingale difference errors. Based on the nonparametric estimates, we derive the least-squares estimator and weighted least-squares estimator of slope parameter, and obtain their moment consistencies under some mild conditions. Finite sample behavior of the estimators is investigated via simulations too.In the following we consider the semiparametric regression model of longitudinal data under martingale difference sequence. We give the estimates for which unknown parameter of β and unknown function of g(·). In certain conditions, the mean square consistencies of p and g(·) are proved.In the end, we consider the semiparametric regression model for longitudinal data with a-mixing errors. We give the estimates for which unknown parameter of p and unknown function of g(·). In certain conditions, the mean square consistencies of p and g(·)are proved.In a word, we get the asymptotic behavior of estimator and other related properties in heteroscedasticity partially linear regression model by some different assumptions and methods.