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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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]