{"paper":{"title":"On boundary detection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Alejandro Cholaquidis, Catherine Aaron","submitted_at":"2016-03-28T17:48:10Z","abstract_excerpt":"Given a sample of a random variable supported by a smooth compact manifold $M\\subset \\mathbb{R}^d$, we propose a test to decide whether the boundary of $M$ is empty or not with no preliminary support estimation. The test statistic is based on the maximal distance between a sample point and the average of its $k_n$-nearest neighbors. We prove that the level of the test can be estimated, that, with probability one, its power is one for $n$ large enough, and that there exists a consistent decision rule. Heuristics for choosing a convenient value for the $k_n$ parameter and identifying observation"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08460","kind":"arxiv","version":3},"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"}