Semi-variable Coefficients Under The Different Data Model Of Statistical Analysis

Semivarying coefficient model, which is also called as semiparametric varying-coefficient partially linear model,was first introduced by Fang and Zhang(2002) to test whether the coefficient functions of the varying coefficient model will truly change.It includes many usual parametric, nonparametric and semiparametric 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 covariates and the response variates and also can avoid many "curse of dimensionality" problems.Therefore, this model has received much attention since its birth, and it has been widely applied in industry, agriculture, finance, geography and some other fields.In the context of classic regression models, we generally assume that the sample data are complete, reliable, and the errors are mutually independent. But in many applications,the assumptions are hard to satisfy because of the nature of measurement mechanism or man-made factor. At least, there always exist measurement errors.So it is more practical to investigate the semivarying coefficient errors-in-variables model.In this paper, first, we discussed the statistical inference of semivarying coefficient model with complete data, then we systematically investigated the estimation procedure of this model for their parametric and nonparametric varying-coefficient part under the case where the covariates are measured with additive errors.One of the main results of the paper was that we discussed the statistical inference of semivarying coefficient model with the independent or the correlated random errors.The second result was that we proposed a new method to estimate the parameters and coefficient functions of the semivarying coefficient errors-in-variables model based on the kernel estimation.The last result was that we did a numerical simulation to test the efficiency of the estimators of the semivarying coefficient model with different data sets.