空间滞后门限回归模型的估计

Estimation of Spatial Lag Threshold Regression Model

为了解决变量空间相关性的存在对模型拟合的影响,捕捉数据截断特征,提高解释力度,提出了一类新的空间滞后门限回归模型,导出其截面极大似然估计量,证明其估计量的大样本性质,Monte Carlo数值模拟了估计量的小样本表现。研究结果表明:(1)大样本情形下,参数估计量具有相合性和渐近正态性;(2)小样本情形下,估计量的精度随样本量的增加而提高,敏感度随样本量的增加而降低;(3)空间复杂程度对空间相关系数的估计量影响较大,对其他估计量的影响较小。该研究结果为空间权重矩阵和样本量的选择提供了有价值的参考。

In order to detect the influence of the existence of spatial correlation and sample splitting feature on the fitting of model and to improve the explanatory power,a new class of spatial lag threshold regression model is proposed.Derive the profile maximum likelihood estimators(PMLEs),prove the large sample property and show their finite sample performances by Monte Carlo simulation.The results are summarized as follows:(1)In large samples,the PMLEs are consistent and the estimators of explanatory variables are asymptotically normal;(2)In finite samples,the precision of estimators increases and the sensitivity of estimators decreases with the growth in sample size;(3)The complexity of spatial weights matrix has a notable impact on the estimator of the spatial correlation coefficient but a weak impact on the other estimators.Besides,a reference is put forward for the selection of appropriate spatial weights matrix and sample size.