Orthogonality based penalized GMM estimation for variable selection in partially linear spatial autoregressive models

Abstract

By combining penalized GMM estimation method with the QR decomposition technique, we propose an orthogonal projection-based regularization estimation method for a class of partially linear spatial autoregressive models. The proposed method can select important covariates in the parametric component, and can also identify the significance of spatial effects. Under some conditions, some theoretical properties are studied, such as the consistency of the proposed variable selection procedure and the oracle property of the resulting estimators for parametric and nonparametric components. Furthermore, some simulation studies are carried out to examine the finite sample performances of the proposed regularization estimation method.