Consistency of bootstrap approximation to the null distributions of local spatial statistics with application to house price analysis

With the increasing availability of spatially extensive geo-referenced data, much attention has been paid to the use of local statistics to identify local patterns of spatial association, in which the null distributions of local statistics play an essential role in the related statistical inference. As a powerful tool to approximate the distribution of a statistic, the bootstrap method is used in this paper to derive null distributions of the commonly used local spatial statistics including local Getis and Ord’s $G_{i}$ G i , Moran’s $I_{i}$ I i and Geary’s $c_{i}$ c i . Strong consistency of the bootstrap approximation to the null distributions of the statistics is proved under some mild conditions, and the Boston housing price data are analyzed to demonstrate the application of the theoretical results.