Assessing spatial autocorrelation (SA) of statistical estimates such as means is a common practice in spatial analysis and statistics. Popular SA statistics implicitly assume that the reliability of the estimates is irrelevant. Users of these SA statistics also ignore the reliability of the estimates. Using empirical and simulated data, we demonstrate that current SA statistics tend to overestimate SA when errors of the estimates are not considered. We argue that when assessing SA of estimates with error, one is essentially comparing distributions in terms of their means and standard errors. Using the concept of the Bhattacharyya coefficient, we proposed the spatial Bhattacharyya coefficient (SBC) and suggested that it should be used to evaluate the SA of estimates together with their errors. A permutation test is proposed to evaluate its significance. We concluded that the SBC more accurately and robustly reflects the magnitude of SA than traditional SA measures by incorporating errors of estimates in the evaluation. Key Words: American Community Survey, Geary ratio, Moran’s I, permutation test, spatial Bhattacharyya coefficient.

中文翻译：

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使用数据可靠性信息测量全局空间自相关

评估统计估计值（例如均值）的空间自相关 (SA) 是空间分析和统计中的常见做法。流行的 SA 统计隐含地假设估计的可靠性是无关紧要的。这些 SA 统计数据的用户也忽略了估计的可靠性。使用经验和模拟数据，我们证明当不考虑估计误差时，当前的 SA 统计数据往往会高估 SA。我们认为，在评估具有误差的估计值的 SA 时，本质上是比较分布的均值和标准误差。使用 Bhattacharyya 系数的概念，我们提出了空间 Bhattacharyya 系数 (SBC)，并建议将其用于评估估计的 SA 及其误差。提出了置换检验来评估其显着性。我们得出结论，通过在评估中纳入估计误差，SBC 比传统 SA 措施更准确、更稳健地反映了 SA 的大小。关键词：美国社区调查，Geary 比率，Moran's I，置换检验，空间 Bhattacharyya 系数。