A Unified Bootstrap Test for Local Patterns of Spatiotemporal Association

Abstract

There has been a growing interest in using local statistics to identify spatial or spatiotemporal association patterns among georeferenced data, in which the null distributions of the statistics play a key role for the confirmatory inferences. In this study we focus on a generic form of local spatiotemporal statistics and propose a unified bootstrap approach to derive the null distribution of the statistic. In particular, the spatiotemporal variants of the commonly used local spatial statistics Moran's Ii, Geary's ci, and Getis and Ord's Gi are studied in detail. Some simulations are conducted to evaluate the validity of the bootstrap method in approximating the null distributions of the three spatiotemporal statistics. Meanwhile, the bootstrap method is compared with the permutation approach in terms of approximation accuracy and computation efficiency. The results show that both the bootstrap and the permutation methods can accurately approximate the null distributions of the statistics for various spatiotemporal topological relationships while the bootstrap method seems to be more efficient than the permutation approach. Additionally, the power of the spatiotemporal version of Moran's Ii in detecting spatiotemporal autocorrelation is empirically assessed and a real-world example is given to demonstrate the application of the bootstrap inference method.