Automatic variable selection for semiparametric spatial autoregressive model

This article studies the generalized method of moment estimation of semiparametric varying coefficient partially linear spatial autoregressive model. The technique of profile least squares is employed and all estimators have explicit formulas which are computationally convenient. We derive the limiting distributions of the proposed estimators for both parametric and non parametric components. Variable selection procedures based on smooth-threshold estimating equations are proposed to automatically eliminate irrelevant parameters and zero varying coefficient functions. Compared to the alternative approaches based on shrinkage penalty, the new method is easily implemented. Oracle properties of the resulting estimators are established. Large amounts of Monte Carlo simulations confirm our theories and demonstrate that the estimators perform reasonably well in finite samples. We also apply the novel methods to an empirical data analysis.