Simulation Research And Application Of Partially Variable Coefficient Spatial Autoregressive Model

At present,with the development of remote sensing technology and geographic information system,the location information contained in spatial data cannot be ignored.In the process of actual data analysis,the data we collect often has regional characteristics.Therefore,the spatial econometric model introduces spatial effects into the model to explore the spatial relationships contained in the data.Spatial econometric models include spatial autoregressive-residual autoregressive model,spatial autoregressive model,spatial error model,etc.Spatial autoregressive model have been studied mostly which consider the linear relationship of dependent and independent variables and the spatial lag between the dependent variables,but in the actual situation,the data not only has a simple linear relationship,but also a functional relationship or maybe a variable coefficient form that cannot be expressed in a specific form.In this thesis,the spatial autoregressive model and the variable coefficient model are combined to form a partial variable coefficient spatial autoregressive model so that the application scope of the model will be further expanded.Further research on partial variable coefficient spatial autoregressive models has practical significance for solving more complex spatial data problems.We mainly discussed the parameter estimation and variable screening problem for partial variable coefficient spatial autoregressive models in this thesis.Since the variable coefficient part is introduced in the model,the likelihood function maximization of the model cannot be solved.Therefore,considering some unknown parameters as the known cross-section likelihood method,in which the variable coefficient part is solved by a more stable B-spline method,the combination of the two methods can effectively solve all the parameters.Because the cross-section likelihood method does not select variables for the model,after all parameters solved,the estimation of the spatial lag coefficient and the variable coefficient part can be substituted into the model.At this point,the model is transformed into a general "linear model".Considering the need to make parameter estimation and variable selection for each variable at the same time,the method used in this thesis is the penalty estimation method,that is,the penalty function is applied to the loss function.The loss function term is based on the square error loss term of the spatial autoregressive model and the minimum model error concluding ALasso,Lasso,and SCAD.In order to visually verify the effectiveness of the method used in this thesis,the numerical simulation of the finite samples is carried out,and the parameter estimates obtained by applying the three penalty functions are compared with the results of the variable selection.The results obtained after the numerical simulation show that the method can effectively identify zero and non-zero coefficients.Finally,the method of this thesis is used for the analysis of practical problems.The empirical analysis includes Boston house price data and college entrance examination score data.The numerous variables are selected and estimated affecting the house price and the college entrance examination scores.It is verified that the model and method can be used to solve the complex data problem existing in reality.