Simulation And Application Of Variable Coefficient Spatial Autoregressive Model

In many recent practical data analysis,the collected data often contain the characteristics of their geographical location.When we analyze and model such data,because of the existence of data correlation,the traditional model is no longer suitable for the analysis of data with spatial characteristics.In order to improve the model,many scholars put forward the spatial autoregressive model to study the spatial data.With the development of the research,the spatial autoregressive model is constantly improving.In order to increase the flexibility of the model and the accuracy of estimation,the variable coefficient part is introduced on the basis of the spatial autoregressive model to construct the variable coefficient spatial autoregressive model.Under the background of large data,the base number of explanatory variables increases,and some minor variables may affect the model.Therefore,the problem of variable selection in variable coefficient spatial autoregressive model has important research significance and practical value.In order to solve the problem of parameter estimation and variable selection in variable coefficient space autoregressive model,we uses quasi-likelihood theory to construct objective function under the whole model,and uses B-spline estimation method to approximate the variable coefficient function and estimate the parameters of the model.Based on the special structure of B-spline estimation method,Group Lasso method is proposed to select variables in model selection.The good properties of the proposed method are studied through simulation study.The results express that the proposed estimation method can accurately estimate the parameters,and the variable selection method can effectively identify non-zero coefficients and zero coefficients.Finally,an example is used to verify the applicability of the methods for parameter estimation and variable selection in variable coefficient space autoregressive model.In the empirical analysis,the influencing factors of Boston house price and China's real estate are studied separately.The valid conclusions are obtained through parameter estimation and variable selection of the model,which verify that the method proposed in this dissertation can solve the problem of parameter estimation and variable selection of variable coefficient spatial autoregressive model in practical problems.