时空加权回归模型的估计及变量选择
[Abstract]:The accuracy of model selection plays an important role in coefficient estimation, data analysis and statistical decision. In recent years, many scholars have put forward different methods for accurate selection of explanatory variables in model building, and have good results in application. However, with the increasing complexity of the data generation mechanism, the simple variable coefficient model can no longer meet the requirements of the data change characteristics, so more factors affecting the data change should be taken into account in the establishment of the model. For the spatio-temporal data, the spatio-temporal weighted regression model (GTWR) gives a reasonable explanation by incorporating the factors of time and geographical location into the coefficients of the explanatory variables. The GTWR model can vividly analyze the dependent relationships between variables. And the change of coefficient function can clearly reflect the spatial and temporal characteristics of data distribution. However, as with other simple models, accurate selection of explanatory variables in the GTWR model is also crucial to the accuracy of the model. Therefore, this paper will study the coefficient representation of GTWR model, the methods and properties of variable selection, and the simulation demonstration. Firstly, based on the principle of least squares, the approximation form of variable coefficient function with space-time characteristic and the local support of spline basis function are given by using spline basis function. The good properties such as unit decomposition make the derivation of theoretical methods more regular in the process of variable selection and the local support of spline basis functions makes the estimation of coefficients more flexible. Secondly, based on the least square objective function, the objective function not only estimates the coefficient function, but also compresses the coefficient function corresponding to the explanatory variable independent of the response variable. The exact model form is determined by eliminating the explanatory variables which are not related to the response variables. At the same time, in order to explain the rationality of the method, the relevant important theorems are proved, and the conclusion shows that the research method is reasonable. Finally, in the part of simulation, this paper first analyzes three different methods of variable selection under the condition of different number of samples, and the results show that, SCAD method is the most accurate method to estimate the coefficient function of the model when the number of samples increases, and the error of the model is the least. Secondly, based on GTWR model, the air quality of 70 cities in China is analyzed from time and space span by using meteorological data. The results show that, whether it is time factor or space factor, Both of them affect the contribution of the explanatory variables to the response variables and present a certain spatio-temporal nonstationarity and the estimated coefficients have better fitting effect at different time points and different regions.
【学位授予单位】:兰州理工大学
【学位级别】:硕士
【学位授予年份】:2017
【分类号】:O212.1
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