Robust Indicators of Spatial Association

2026-07-08

AI Summary

This study addresses the susceptibility of the conventional Moran’s I statistic to distributional outliers, which can introduce bias in both global and local spatial autocorrelation estimates. The authors systematically evaluate and compare three classes of robust estimation methods—plug-in robust estimators, trimmed least squares (TLS), and Theil–Sen–type estimators—for constructing robust Moran indices and LISA maps, accompanied by tailored visualization strategies. This work presents the first comprehensive comparison of multiple robust spatial association measures and proposes the Theil–Sen Moran estimator as a preferred default for exploratory spatial data analysis. Empirical results demonstrate its superior performance across diverse scenarios, while plug-in methods also exhibit strong scalability and reliability in large datasets, collectively enhancing the robustness of spatial outlier detection.

Abstract

The Moran statistic, and its accompanying local statistics, are one of the most extensively used exploratory spatial data analysis tools for assessing global and local spatial autocorrelation. The paired visualizations for these statistics, the Moran Scatterplot and LISA map, are likewise central to spatial analysis. Together, these statistics and visualizations are used to identify spatial clusters, regions of a map where observations are similar to one another, or spatial outliers, observations that differ sharply from their surroundings. However, the use of Moran statistics to detect spatial outliers is complicated by their high sensitivity to *distributional* outliers: observations that are extreme relative to the overall data distribution, regardless of their spatial context. Indeed, a single distributional outlier can (I) distort local statistics across the entire map and (II) bias the global estimate of spatial association. Recent work has begun to address (I) and (II) separately using plug-in robust estimators for location, scale, and spatial correlation. In this paper, we offer the first systematic evaluation of robust LISA and global spatial association measures, using variety of plug-in robust estimators, a trimmed least squares (TLS) estimator, and a Theil-Sen-style estimator. We also outline a visualization strategy to create Robust Moran Scatterplots/LISA maps for each. Out of all considered approaches, we find that the Theil-Sen Moran estimator is a better default for exploratory spatial data analysis and visualization, while robust plug-in estimators also offer acceptable performance in large datasets.

Problem

• spatial outliers
• distributional outliers
• Moran statistic
• spatial autocorrelation
• robust estimation

Innovation

• robust spatial statistics
• Moran's I
• Theil-Sen estimator
• spatial outliers
• LISA