Theil-Sen Estimation for Moran's I: A Robust Representation and Estimation Approach

The OLS-derived local Moran estimator is extensively studied. Yet, few have focused on whether it may be possible to estimate local Moran statistics in a statistically-robust fashion. Indeed, robustness is important when trying to distinguish between spatial outliers, which are unusual observations relative to other observations within a geographic locale, and distributional outliers, which are unusual observations no matter where they are or who they’re around. We show how robust Moran estimation actually involves two problems: (I) how do we robustly represent the surroundings of each site? and, (II) how do we robustly estimate the relationship between sites and their surroundings? We show that an optimally-robust estimator, the Trimmed Least Squares estimator, and the Theil-Sen estimator solve both representation and estimation issues fairly well. We posit that the Theil-Sen estimator should be explored as a default estimator for local and global Moran’s I statistics.