Robust Variable Selection with Exponential Squared Loss for the Spatial Durbin Model

With the continuous application of spatial dependent data in various fields, spatial econometric models have attracted more and more attention. In this paper, a robust variable selection method based on exponential squared loss and adaptive lasso is proposed for the spatial Durbin model. Under mild conditions, we establish the asymptotic and "Oracle" properties of the proposed estimator. However, in model solving, nonconvex and nondifferentiable programming problems bring challenges to solving algorithms. To solve this problem effectively, we design a BCD algorithm and give a DC decomposition of the exponential squared loss. Numerical simulation results show that the method is more robust and accurate than existing variable selection methods when noise is present. In addition, we also apply the model to the 1978 housing price dataset in the Baltimore area.