{"paper":{"title":"The limit of finite sample breakdown point of Tukey's halfspace median for general data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Shihua Luo, Xiaohui Liu, Yijun Zuo","submitted_at":"2016-04-25T01:49:34Z","abstract_excerpt":"Under special conditions on data set and underlying distribution, the limit of finite sample breakdown point of Tukey's halfspace median ($\\frac{1} {3}$) has been obtained in literature. In this paper, we establish the result under \\emph{weaker assumption} imposed on underlying distribution (halfspace symmetry) and on data set (not necessary in general position). The representation of Tukey's sample depth regions for data set \\emph{not necessary in general position} is also obtained, as a by-product of our derivation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.07104","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":""},"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"}