{"paper":{"title":"The broken sample problem revisited: Proof of a conjecture by Bai-Hsing and high-dimensional extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","stat.TH"],"primary_cat":"math.ST","authors_text":"Jiaming Xu, Simiao Jiao, Yihong Wu","submitted_at":"2025-03-18T18:15:13Z","abstract_excerpt":"We revisit the classical broken sample problem: Two samples of i.i.d. data points $\\mathbf{X}=\\{X_1,\\cdots, X_n\\}$ and $\\mathbf{Y}=\\{Y_1,\\cdots,Y_m\\}$ are observed without correspondence with $m\\leq n$. Under the null hypothesis, $\\mathbf{X}$ and $\\mathbf{Y}$ are independent. Under the alternative hypothesis, $\\mathbf{Y}$ is correlated with a random subsample of $\\mathbf{X}$, in the sense that $(X_{\\pi(i)},Y_i)$'s are drawn independently from some bivariate distribution for some latent injection $\\pi:[m] \\to [n]$. Originally introduced by DeGroot, Feder, and Goel (1971) to model matching recor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.14619","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/2503.14619/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"}