空间滞后模型中Moran's I统计量的Bootstrap检验

Bootstrap Moran's I test statistic in spatial autoregressive models

针对空间滞后模型的估计残差,采用Wild.Bootstrap方法进行空间相关性检验;进而,基于Moran's I统计量的经验分布,从水平扭曲和功效角度比较Bootstrap检验和渐近检验的有效性.Monte Carlo实验结果显示,在经典正态假设条件下,Bootstrap检验已然同等或优于渐近检验;在更为实际的异方差、非正态假设条件下,渐近检验显著偏离,而Bootstrap检验的水平扭曲更小、功效更高.当模型不满足经典的分布假设条件,尤其是在小样本和空间衔接密度较高情况下,与渐近检验相比,Bootstrap检验更为有效.

In this paper, residual-based wild Bootstrap methods are applied for hypothesis testing of spatial correlation in a spatial autoregressive linear regression model. Based on the empirical distribution of Moran＇s I test statistic, the actual size and power of Bootstrap and asymptotic tests for spatial correlation are evaluated and compared. Under classical normality assumption of the model, the performance of the Bootstrap tests is equivalent to or better than that of the asymptotic tests in terms of size and power. For more realistic heterogeneous non-normal distributional models, size distortion of the asymptotic tests is far away from the theoretical zero value. Whereas, Bootstrap tests have shown superiority in smaller size distortion and higher power when compared to asymptotic counterparts. Monte Carlo experiments indicate that based on Moran＇s I test statistic, Bootstrap method is an effective alternative to the theoretical asymptotic approach, especially for cases with a small sample and dense spatial contiguity when the classical distributional assumption is not warranted in a spatial autoregressive model.