The Size and Power of Bootstrap Tests for Spatial Dependence in a Linear Regression Model

Abstract

In this paper, we define the spatial bootstrap test as a residual-based bootstrap method for hypothesis testing of spatial dependence in a linear regression model. Based on Moran’s I statistic, the empirical size and power of bootstrap and asymptotic tests for spatial dependence are evaluated and compared. Under classical normality assumption of the model, the performance of the spatial bootstrap test is equivalent to that of the asymptotic test in terms of size and power. For more realistic heterogeneous non-normal distributional models, the applicability of asymptotic normal tests is questionable. Instead, spatial bootstrap tests have shown superiority in smaller size distortion and higher power when compared to asymptotic counterparts, especially for cases with a small sample and dense spatial contiguity. Our Monte Carlo experiments indicate that the spatial bootstrap test is an effective alternative to the theoretical asymptotic approach when the classical distributional assumption is violated.