{"paper":{"title":"Minimax convergence rate for estimating the Wasserstein barycenter of random measures on the real line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Alfredo L\\'opez, J\\'er\\'emie Bigot, Ra\\'ul Gouet, Thierry Klein","submitted_at":"2016-06-13T13:10:03Z","abstract_excerpt":"This paper is focused on the statistical analysis of probability measures $\\nu_{1},\\ldots,\\nu_{n}$ on $\\mathbb{R}$ that can be viewed as independent realizations of an underlying stochastic process. We consider the situation of practical importance where the random measures $\\nu_{i}$ are absolutely continuous with densities $f_{i}$ that are not directly observable. In this case, instead of the densities, we have access to datasets of real random variables $(X_{i,j})_{1 \\leq i \\leq n; \\; 1 \\leq j \\leq p_{i} }$ organized in the form of $n$ experimental units, such that $X_{i,1},\\ldots,X_{i,p_{i}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03933","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}