Variable Selection For Partially Linear Spatial Autoregressive Models With A Diverging Number Of Parameters

In economics,regional science and geography,spatial models play an important role in the analysis of empirical problems.One of the most popular is spatial autoregressive model,which can solve the common spatial dependence and spatial autocorrelation characteristics of spatial data.The traditional spatial autoregressive model considers that all regression variables have linear effects on dependent variables,but the presence of nonlinear components will make the estimation error of dependent variables larger.With the rapid development of computer technology,people have obtained a huge amount of observation data,and variable selection has become one of the hot spots of modern statistical analysis.To sum up,we study the variable selection problem in partially linear spatial autoregressive model with a diverging number of parameters.In this dissertation,B-spline basis functions are used to approximate nonlinear functions and instrumental variables are used to deal with endogenous spatial lag terms.In this method,the complex model is firstly transformed into a classical linear model,and then SCAD penalty is introduced into the model.At the same time,variable selection and regression coefficient estimation are carried out,and the penalty least square estimation is obtained.Under the regularity condition,the consistency and Oracle property of the penalty estimation are established,and the optimal convergence rate of the nonlinear function is obtained.Through the simulation study,it is verified that the new penalized least square estimation method can effectively identify the non-zero coefficients and zero coefficients,and it is illustrated with the actual data.In addition,the penalty likelihood ratio test statistics are discussed briefly,and their asymptotic distribution under the null hypothesis is obtained by adding some mild conditions to the penalty function.