{"paper":{"title":"Geometrical and statistical properties of M-estimates of scatter on Grassmann manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","stat.TH"],"primary_cat":"math.ST","authors_text":"Christian Mazza, Corina Ciobotaru","submitted_at":"2018-12-30T20:26:11Z","abstract_excerpt":"We consider data from the Grassmann manifold $G(m,r)$ of all vector subspaces of dimension $r$ of $\\mathbb{R}^m$, and focus on the Grassmannian statistical model which is of common use in signal processing and statistics. Canonical Grassmannian distributions $\\mathbb{G}_{\\Sigma}$ on $G(m,r)$ are indexed by parameters $\\Sigma$ from the manifold $\\mathcal{M}= Pos_{sym}^{1}(m)$ of positive definite symmetric matrices of determinant $1$. Robust M-estimates of scatter (GE) for general probability measures $\\mathcal{P}$ on $G(m,r)$ are studied. Such estimators are defined to be the maximizers of the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.11605","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1812.11605/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"}