{"paper":{"title":"Level sets estimation and Vorob'ev expectation of random compact sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"CMAP), Philippe Heinrich (LPP), Radu Stefan Stoica (LPP), Viet Chi Tran (LPP","submitted_at":"2010-06-26T13:26:56Z","abstract_excerpt":"The issue of a \"mean shape\" of a random set $X$ often arises, in particular in image analysis and pattern detection. There is no canonical definition but one possible approach is the so-called Vorob'ev expectation $\\E_V(X)$, which is closely linked to quantile sets. In this paper, we propose a consistent and ready to use estimator of $\\E_V(X)$ built from independent copies of $X$ with spatial discretization. The control of discretization errors is handled with a mild regularity assumption on the boundary of $X$: a not too large 'box counting' dimension. Some examples are developed and an appli"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.5135","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"}