Estimation Of A Partially Linear Varying-coefficient EV Model Under Restricted Condition

Partially linear varying-coefficient model, which has recently been proposed as a new model, holds ample contents and extensive applications. It includes many usual parametric, nonparametric and semi-parametric regression models.The new model have the merits of the linear model which are prone to easily interpretation and can display robust virtue as for nonparametric models. Besides, it can dynamically describe the relation between the covariables and the response variables.In the context of classic regression models, we generally assume that the sam-ple data are complete, reliable, and the errors are mutually independent, Howev-er, in practice, the data always has the measurement errors. the partially linear varying-coefficient models introduced in this paper are based on the data with mea-surement errors. Due to the conditions or hypothesis in the actual problem, the parameters of the model have certain restraints. In this paper,the partially linear varying-coefficient models under restricted condition are discussed,the estimates of the coefficient functions and the constant coefficient,their asymptotical are studied.In Chapter1, we mainly introduce the background and development situation of the subject, and give some theoretical tools and preliminaries serving the discussion in the paper.In Chapter2, we investigate the estimation of partially linear varying-coefficient EV models under restricted condition. The estimators of parametric and nonpara-metric components are established based on adjust weighted least-squares met hod, and their consistency are also studied under some regularity conditions.Some simulation studies are carried out to assess the performance of the proposed methods.In Chapter3, In this paper,we study a partially linear varying-coefficient errors-in-variables (EV) model under additional restricted condition. Both of the parametric and nonparametric components are measured with additive errors. The restricted estimators of parametric and nonparametric components are established based on modified profile least-squares method and local correction method.and their asymp-totic properties are also studied under some regularity conditions.Some simulation studies are conducted to illustrate our approaches.