Simultaneous estimation and domain selection for the spatial autoregressive model with semi-parametric functional coefficients

This paper considers simultaneous estimation and selection of the spatial autoregressive model with semi-parametric functional coefficients, which not only allows for cross-sectional dependence but also adapts the relationship between predictors and response over different domains of interest, such as time. In contrast to the conventional variable selection procedure focusing on entire region, our proposed method is designed for identification of subregions on which the functional coefficients are zero, to deeply learn the local sparsity of dynamic effects of the significant predictors, as well as to achieve more interpretable estimation at the meantime. Towards this goal, the smoothing spline approximation, regularization mechanism and generalized method of moments estimation approach are incorporated into one framework. Asymptotic properties of the resulting estimator are rigorously established under some regularity conditions, and a practical iterative algorithm is provided for implementation. Abundant simulation studies confirm the theoretical results and superior performance of the proposed method, when compared to other competitors. Three empirical examples are analyzed for practical applications.