The Study Of The Two-step Estimation's For Multivariate Regression Model

Semi-parametric spatially varying-coefficient regression model is widely used in geography, weather, economic conditions, geology and other fields of data analysis, and it is an effective tool for spatial data analysis and processing. It builds on base of the linear regression model and nonparametric regression model, combining the advantages of both. Parameter components are used in analyzing of uncertainty factors, and non-parametric components are used in analyzing of random interference factors. Semi-parametric spatially varying-coefficient regression model can not only model the real world, but can analyze the potential law by the model. Therefore, it is not only academic significance but also a wide range of application that we further study about semi-parametric spatially varying-coefficient regression model.This research work mainly in the following three aspects: (a) Two-step procedure for semi-parametric spatially varying-coefficient regression model. By improving the traditional semi-parametric spatially varying-coefficient regression model, a new model is built and its two-step procedure are made in this paper. We have analyzed the robustness of initial estimator of variable coefficients in two-step procedure according to weighted least squares. The results show that the sum of squares of deviations has been reduced, are conducive to enhancing the robustness of estimators. (b) Test of significance to two-step procedure for variable coefficients. The improved semi-parametric spatially varying-coefficient regression model, for variable coefficients part of its two-step procedure, we adopt a general hypothesis testing, quasi-regression equation significance testing and significance testing of coefficients, and test the significance for first estimator of variable coefficients by t ? distribution. It can effectively reduce the system error and increase the robustness of the significance testing. (c) Discuss admissibility of the initial estimate of variable coefficients. For two-step procedure of the improved semi-parametric spatially varying-coefficient regression model, in this paper, we have discussed admissibility of the initial estimate of variable coefficients, and obtained the necessary and sufficient conditions of initial estimator of variable coefficients.