{"paper":{"title":"Strong Consistency of Frechet Sample Mean Sets for Graph-Valued Random Variables","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["q-bio.QM","stat.ME","stat.TH"],"primary_cat":"math.ST","authors_text":"Cedric E. Ginestet","submitted_at":"2012-04-14T15:37:04Z","abstract_excerpt":"The Frechet mean or barycenter generalizes the idea of averaging in spaces where pairwise addition is not well-defined. In general metric spaces, the Frechet sample mean is not a consistent estimator of the theoretical Frechet mean. For graph-valued random variables, for instance, the Frechet sample mean may fail to converge to a unique value. Hence, it becomes necessary to consider the convergence of sequences of sets of graphs. We show that a specific type of almost sure convergence for the Frechet sample mean previously introduced by Ziezold (1977) is, in fact, equivalent to the Kuratowski "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3183","kind":"arxiv","version":4},"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"}