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.