Robust Variable Selection with Exponential Squared Loss for the Spatial Single-Index Varying-Coefficient Model

As spatial correlation and heterogeneity often coincide in the data, we propose a spatial single-index varying-coefficient model. For the model, in this paper, a robust variable selection method based on spline estimation and exponential squared loss is offered to estimate parameters and identify significant variables. We establish the theoretical properties under some regularity conditions. A block coordinate descent (BCD) algorithm with the concave–convex process (CCCP) is composed uniquely for solving algorithms. Simulations show that our methods perform well even though observations are noisy or the estimated spatial mass matrix is inaccurate.