Theoretical Research And Empirical Analysis Of Variable Selection In Spatial Autoregressive Model

In recent decades,with the in-depth study of economic issues,people have found that spatial factors have a growing influence on economic issues.Therefore,the research field of spatial statistics has emerged,which attracts not only the focus of econometricians,but also the attention of statisticians.Among a large number of spatial statistical research issues,a type of statistical model?spatial autoregressive model has become the target of many statisticians.With the rapid development of computer technology,it is easier for people to obtain largescale observation data.It contains two meanings: one is the huge sample size,and the other is that each sample can contain more information.How to deal with Data,and then obtain the most valuable information,makes variable selection problem one of the hot topics of modern statistical analysis.In this context,this paper combines two parts discussed above and studies the following issues:First,under the minimum prediction error criterion,the linear spatial autoregressive model is studied for compressive estimation.Firstly,based on an excellent initial estimate,a new loss function is constructed from the perspective of prediction.this method can do variable selection and parameter estimation simultaneously by punishing the loss function proposed.And we prove that the new estimator enjoys consistency and Oracle properties under the SCAD penalty function.Secondly,through the simulation results,it is verified that the proposed estimation method can effectively identify non-zero coefficients and zero coefficients.Finally,this estimation method is applied to the classic boston housing price data and urban air quality data,further validating the practicability of this method.Second,under the least mean square error criterion,variable selection of partially linear spatial autoregressive model is studied.Firstly,for the nonlinear part of the model,it is linearized by B-spline method,and then the spatial lag term with endogeneity is dealt with instrumental variable method.In this way,the complex partial linear spatial autoregressive model can be transformed into a classical linear model,and then do variable selection.Secondly,the numerical simulation of different penalty functions LASSO,ALASSO,SCAD is done.Conclusions are drawn from it: the estimation method proposed in this paper can effectively identify nonzero coefficients and zero coefficients;simulation results show that estimations under SCAD penalties have better results than those obtained under other penalties;Under the SCAD penalty function,estimations obtained for different initial values of spatial lag coefficient perform well.Finally,the proposed method is applied to analysis of urban air quality data,and obtains the same as results those obtained by environmental administration.