Wang Yezi, Wang Zhijian, Song Yunquan
College of Science, China University of Petroleum, Qingdao 266580, China.
Entropy (Basel). 2023 Jan 26;25(2):230. doi: 10.3390/e25020230.
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.
由于空间相关性和异质性在数据中常常同时出现，我们提出了一种空间单指标变系数模型。针对该模型，本文提供了一种基于样条估计和指数平方损失的稳健变量选择方法来估计参数并识别显著变量。我们在一些正则条件下建立了理论性质。独特地构造了一种带有凹凸过程（CCCP）的块坐标下降（BCD）算法来求解算法。模拟结果表明，即使观测值存在噪声或者估计的空间质量矩阵不准确，我们的方法也能表现良好。
