{"paper":{"title":"Estimating the Wasserstein barycenter of one-dimensional distributions under sparse sampling","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Florian Stijven, James Peng, Linbo Wang, Peter B. Gilbert","submitted_at":"2026-06-08T19:22:01Z","abstract_excerpt":"We study distributional data under sparse sampling where each unit is represented by a probability distribution on the real line observed only through a small i.i.d.~sample. A natural notion of central tendency for one-dimensional distributional data is the Wasserstein barycenter, whose quantile function is the pointwise average of the unit-level quantile functions. We focus on pointwise estimation of the Wasserstein barycenter quantile function: at a given quantile level, the target is the population mean of the corresponding unit-level quantiles. A naive plug-in estimator is the empirical Wa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.10096","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.10096/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}