On Heterogeneity in Wasserstein Space

Kisung You

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arXiv · 2603.14815

On Heterogeneity in Wasserstein Space

Kisung You

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Abstract

Data represented by probability measures arise as empirical distributions, posterior distributions, and feature-based representations of complex objects. We study heterogeneity in a population of probability measures through the expected value of a chosen transform of the pairwise Wasserstein distance. The resulting estimator is unbiased and, under simple moment conditions on the population law, is strongly consistent, asymptotically normal, and equipped with a consistent standard error. This also yields a simple comparison of two populations and remains stable under plug-in approximation when the measures are estimated. The associated empirical eccentricities identify the observations that contribute most strongly to heterogeneity within a sample.

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Kisung You. 2026-03-16. On Heterogeneity in Wasserstein Space. https://arxiv.org/abs/2603.14815

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