Statistical Inference For Varying Coefficient Higher-order Spatial Autoregressive Models

As the demand for spatial data analysis is rapidly increasing,spatial statistical models especially spatial autoregressive models have received widespread attention.However,most of the existing spatial autoregressive models are linear models or first-order nonlinear models.For the former,although the linear model has the advantages of simple form and strong explanation power,it has the risk of model misspecification,and ignores dynamic feature that may exist in spatial data.Although the latter makes up for the shortcomings of the linear model,it can only describe single type of spatial correlation,which limits the practical application effect of the model.In order to meet the needs of theoretical research and practical application,we have carried out the following work:In order to capture the dynamic features of spatial data and describe various types of spatial correlation,a varying coefficient high-order spatial autoregressive model is proposed by setting the regression coefficient in the linear high-order spatial autoregression model as a function of a variable(smooth variable).By combining the sieve method and the two-stage least squares method,a sieve two-stage least squares method for the proposed model is constructed,and the asymptotic properties of the obtained estimators are derived under appropriate conditions.In addition,two hypothesis testing methods are proposed to check appropriateness of certain linear constraint condition on the spatial autoregressive parameters and constancy of the coefficient functions,respectively.A series of numerical simulation studies show that the proposed estimation method and testing methods perform well in finite samples,and the Boston house price data are analyzed to demonstrate the proposed model and its estimation and testing methods well.In order to make the varying coefficient high-order spatial autoregressive model more suitable for practical applications,the structure identification and variable selection of the model are studied.By combining the sieve method,two-stage least squares method and penalty function,a variable selection method is established to estimate unknown parameters,identify the real model and select important variables simultaneously.The appropriate spatial weight matrices are selected by penalizing the spatial autoregressive coefficient;important explanatory variables are selected by penalizing coefficient function;the first derivative of the penalty coefficient function is used to identify the potential constant coefficient.Under appropriate conditions,the asymptotic property of the obtained estimator and proves is established that the method has Oracle property.A series of numerical simulation simulation studies show that the proposed variable selection method performs well,and the Boston house price data are analyzed to demonstrate the proposed method.