Orthogonal projection based variable selection for semiparametric spatial autoregressive models

In this paper, we consider the variable selection for a class of semiparametric spatial autoregressive models. By using orthogonal projection technique, we propose a new orthogonality-based variable selection procedure, which can select important covariates, and can identify the significance of spatial effects simultaneously. The consistency of the proposed variable selection procedure and the convergence rate of the resulting estimators are derived under some regular conditions. Furthermore, some simulation studies are carried out to examine the finite sample performance of the proposed method.