Factor Adjusted Variable Selection For Linear Spatial Autoregressive Model

With the deepening research on economic regional science and geography,spatial model is becoming important for practical problems.The most studied spatial autoregressive model can be used to solve the problem of spatial dependence.With the rapid development of science and technology,it is easy to obtain observation data with high dimension and large scale.Most commonly-used model selection methods fail to consistently recover the true model when the covariates are highly correlated.Motivated by factor analysis,we consider the case where covariate dependence can be reduced through the factor model and propose a consistency strategy named Factor-Adjusted Regularized Model Selection based on Spatial Autoregressive Model.This paper adopts the variable selection method based on factor model,which can effectively deal with the correlation between covariables and achieve variable selection.In the first step,we transformed the basic model into a classical linear model,then the covariates of the model are replaced by latent factors and idiosyncratic components.Next,the Alasso penalty is introduced to realize variable selection and parameter estimation at the same time.In additon,under some regular conditions,Oracle properties of the penalty estimator is established and proved.Finally,the simulation study shows the proposed method identify non-zero coefficients and zero coefficients.