Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: You, Kisung
Institution: Baruch College
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7138437568
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