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.

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.

Variable Selection of Spatial Logistic Autoregressive Model with Linear Constraints.

In recent years, spatial data widely exist in various fields such as finance, geology, environment, and natural science. These data collected by many scholars often have geographical characteristics. The spatial autoregressive model is a general method to describe the spatial correlations among observation units in spatial econometrics. The spatial logistic autoregressive model augments the conventional logistic regression model with an extra network structure when the spatial response variables are discrete, which enhances classification precision. In many application fields, prior knowledge can be formulated as constraints on the parameters to improve the effectiveness of variable selection and estimation. This paper proposes a variable selection method with linear constraints for the high-dimensional spatial logistic autoregressive model in order to integrate the prior information into the model selection. Monte Carlo experiments are provided to analyze the performance of our proposed method under finite samples. The results show that the method can effectively screen out insignificant variables and give the corresponding coefficient estimates of significant variables simultaneously. As an empirical illustration, we apply our method to land area data.