Sparse Estimation Of Partially Linear Additive Spatial Autoregressive Model

Spatial autoregressive model is a hot topic in current econometrics,because it considers the spatial correlation between the data,and the theoretical research and statistical inference methods of this model are very mature.However,the general spatial autoregressive model only considers the linear relationship,so the spatial autoregressive model is not applicable in some cases involving nonlinear relationship.Many scholars began to study how to add the non-parametric functions into spatial autoregressive model to form more flexible and effective model to fit the corresponding spatial autocorrelation data.This paper studies the estimation and variable selection of partially linear additive autoregressive model.In order to estimate the unknown spatial lag coefficient,constant coefficient and additive function in the model,we use the B-spline basis function to approximate the nonparametric function.Meanwhile,the technique of instrumental variables is introduced into the estimation program to remove the estimation bias caused by endogenous variables.All the unknown components in the model can be estimated via a simple one-step estimation algorithm.For the variable selection of parametric part,we propose a penalized loss function based on SCAD penalty to select the significant components.The effectiveness of estimation and variable selection method is verified by some Monte Carlo simulations.Finally,the proposed approach is further applied to analyze the Boston housing price data.