{"paper":{"title":"On the convergence of Maronna's $M$-estimators of scatter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.AP","authors_text":"Frederic Pascal, Romain Couillet, Yacine Chitour","submitted_at":"2014-03-24T14:50:09Z","abstract_excerpt":"In this paper, {we propose an alternative proof for the uniqueness} of Maronna's $M$-estimator of scatter (Maronna, 1976) for $N$ vector observations $\\mathbf y_1,...,\\mathbf y_N\\in\\mathbb R^m$ under a mild constraint of linear independence of any subset of $m$ of these vectors. This entails in particular almost sure uniqueness for random vectors $\\mathbf y_i$ with a density as long as $N>m$. {This approach allows to establish further relations that demonstrate that a properly normalized Tyler's $M$-estimator of scatter (Tyler, 1987) can be considered as a limit of Maronna's $M$-estimator. Mor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5977","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"}