空间滞后单指标变系数模型的估计及其应用

Estimation and Application for Spatial Lag Single Index Variable-Coefficient Model

研究目标:处理数据中同时存在的空间相关性和空间异质性。研究方法:本文提出了一种空间滞后单指标变系数模型,结合样条估计法和极大似然估计法构建了模型参数的估计方法,证明了估计量的一致性与渐近正态性。研究发现:采用Monte-Carlo模拟探究估计方法在有限样本下的表现,模拟结果表明模型估计量具有优良的表现,通过对比不同样本容量混合误差项方差,估计量的精度随着样本容量的增加而提高,随着误差项方差的减小而提高,且不同的空间相关系数下估计量仍然具有较高的精度,体现出估计方法的稳健性。研究创新:将空间滞后单指标变系数模型应用于环境污染分析中,结果表明空间滞后单指标变系数模型拟合效果优于多元线性回归模型和空间滞后模型,证实了模型的适用性。研究价值:空间滞后单指标变系数模型能够同时处理数据存在的空间相关性和空间异质性,拟合效果精确,为决策者提供更好的决策参考。

Research Objectives: In order to deal with the spatial correlation and spatial heterogeneity existing in the data. Research Methods: This paper proposes a spatial lag single index variable-coefficient model, combines the spline estimation method and the maximum likelihood estimation method to construct the estimation method of the model parameters, and proves the consistency and asymptotic normality of the estimator. Research Findings: Monte-Carlo simulation is used to explore the performance of the estimation method under limited samples. The simulation results show that the model estimator has excellent performance. By comparing the variance of the mixed error term of different sample sizes, the accuracy of the estimator increases as the sample size increases, and as the error term variance decreases, and the estimator still has high accuracy under different spatial correlation coefficients, which reflects the robustness of the estimation method. Research Innovations: The spatial lag single index variable coefficient model is applied to environmental pollution analysis. The results show that the fitting effect of the spatial lag single index variable coefficient model is better than the multiple linear regression model and the spatial lag model.It confirms the applicability of the model. Research Value: The spatial lag single index variable coefficient model can deal with the spatial correlation and spatial difference of the data. The fitting effect is accurate and provides better decision-making reference for decision-makers.