Comparison of Local Spatial Deviation Indicators with Their Associated Tests: Evidence from Simulations and Applied Cases

Currently, two kinds of local spatial deviation indicators, namely local spatial heteroscedastic statistics and local spatial variance, with their associated tests have been proposed for estimating and inferring the characteristics of a spatial process at the second-order moment level, which is of wide potential application in spatial data analysis. Nonetheless, the performance of the indicators with their associated tests remains to be systematically investigated. Due to their mixed application orientations and the difficulty in theoretically comparing their performance, we design proper simulation experiments to assess their performance in estimating the variance function of a spatial process and detecting the local spatial heteroscedasticity and the boundaries of spatial homogeneous clusters. Some worthwhile findings are obtained and their performance from different application orientations is clarified. Based on the findings, two real-life spatial datasets are analyzed to demonstrate the applications of the indicators with their associated tests.