Part Of The Linear Regression Model Estimated

Including parametric component and non-paramertic component, partially linear regression models allow easier interpretation of the effect on each variable, so they are more flexible and universal than the classic linear models or non-paramertic regression models. Engle, Grabger, Rice and Weiss were among the first to consider the partially linear regression models. In 1986, they analyzed the ralationship between temperature and electricity usage. From then on, there have been maken great progress in the studies on partially linear models. In this paper, the consistency and asymptotic normality of the estimators are studied on the base of domestic and overseas scholar researches.Firstly, the partially linear regression models are introduced from the origin to the development at home and abroad, mainly including all kinds of estimation methods to parametric component and non-parametric component and studies to the properties of large sample. The studies are based on the different supposes to the errors in the models with fixed designed points.Secondly, considering the partially linear models with linear process errors Bying least squares and usual weighted function method combining two-stage estimation, we define the estimatorsβand g forβand g(·), then we obtain their r-order mean consistency, complete consistency and asymptotic normality under suitable conditions. Since given conditions become weaker, the means in this paper are more universal and flexible than other methods, there we remove some restrictions on logrithm calculation, and introduce some Iimite properties on power function.Finally, to the above model withρ-mixing sequence, we use Wavelet methods and obtain the estimators of/βand g(·), then we study the r-order consistency of the estimators.