ABSTRACT Moran's I statistic [Moran, (1950), ‘Notes on Continuous Stochastic Phenomena’, Biometrika, 37, 17–23] has been widely used to evaluate spatial autocorrelation. This paper is concerned with Moran's I-induced testing procedure in residual analysis. We begin with exploring the Moran's I statistic in both its original and extended forms analytically and numerically. We demonstrate that the magnitude of the statistic in general depends not only on the underlying correlation but also on certain heterogeneity in the individual observations. One should exercise caution when interpreting the outcome on correlation by the Moran's I-induced procedure. On the other hand, the effect on the Moran's I due to heterogeneity in the observations enables a regression model checking procedure with the residuals. This novel application of Moran's I is justified by simulation and illustrated by an analysis of wildfire records from Alberta, Canada.

中文翻译：

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Moran's I 基于统计的非参数检验与时空观察

摘要 Moran's I 统计量 [Moran, (1950), 'Notes on Continuous Stochastic Phenomena', Biometrika, 37, 17–23] 已被广泛用于评估空间自相关。本文涉及残差分析中的 Moran 的 I 诱导检验程序。我们首先从分析和数值上探索 Moran's I 统计量的原始和扩展形式。我们证明统计量的大小通常不仅取决于潜在的相关性，还取决于个别观察中的某些异质性。在解释 Moran's I 诱导程序的相关性结果时，应谨慎行事。另一方面，由于观察中的异质性对 Moran's I 的影响使回归模型检查程序与残差成为可能。