Parameter Estimation And Application Research Of Geographically And Temporally Weighted Regression Model

In recent years, with the frequent appearance of massive data and the increasing complexity of data generation mechanism, assuming that the data structure has some consistency and the regression function possesses a particular parametric form has no longer adapted the analysis of complex data. In this context, non-parametric re-gression model with a high degree of flexibility and adaptability is generated. In the numerous non-parametric regression models, varying coefficient regression model as a useful extension of the classical linear regression model, has received wide attention and been extensively used. Geographically weighted regression (GWR) model as one of the spatial varying coefficient regression models, can not only probe the changes of coefficients but also interpret significant of its changes. Therefore the proposing and application of geographically weighted regression model has a great impact. By incorporating temporal effects into the geographically weighted regression model, an extended GWR model, geographically and temporally weighted regression(GTWR) model, has been developed to deal with both spatial and temporal nonstationari-ty simultaneously. The fitting method, finite sample properties of estimators and application of geographically and temporally weighted regression model have been researched in this article.Based on the theory of weighted least squares estimate, the fitting method of geographically and temporally weighted regression model is given, the related select principle of weight function and cross-validation for fixing bandwidth parameters are also provided. Combining local linear estimation and GTWR fitting method, local linear estimation method and finite sample properties of geographically and tempo-rally weighted regression model are given, and by comparing with GTWR method, we show that the local linear estimation method improves the estimated effect of the coefficient functions and the error variance. The two-step estimation procedure of geographically and temporally weighted regression model is given on the basis of local linear estimation. But the drawback of the two-step estimation procedure is large computation. In order to repair this drawback, an improved two-step estimation pro-cedure is proposed and the approximation of the conditional bias and its estimation and the approximation of the conditional variance of local linear estimator of the coefficient functions are given respectively.Finally, we use geographically and temporally weighted regression model to study an instance of Meteorology. In order to test the performance of the local linear estimation method and two-step estimation method, based on the meteorological data, geographically and temporally weighted regression model is used to simulate the relationship among air quality index, temperature and precipitation. And then analyze the temporal and spatial distribution characteristic of air quality index. The results show that the local linear estimation method and two-step estimation method have good effects and the performance of geographically and temporally weighted regression model is favorable in the practical application.