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Moreover, our estimator can be made to be optimally robust to adversarial contamination. This result improves the recent contributions by Mendelson and Zhivotovskiy and Catoni and Giulini, and matches parallel work by Abdalla and Zhivotovskiy (the exact relationship with this last work is described in the paper).<\/jats:p>","DOI":"10.1214\/24-aos2407","type":"journal-article","created":{"date-parts":[[2024,11,21]],"date-time":"2024-11-21T01:25:56Z","timestamp":1732152356000},"page":"1953-1977","source":"Crossref","is-referenced-by-count":6,"title":["Improved covariance estimation: Optimal robustness and sub-Gaussian guarantees under heavy tails"],"prefix":"10.1214","volume":"52","author":[{"given":"Roberto I.","family":"Oliveira","sequence":"first","affiliation":[{"name":"Instituto de Matem\u00e1tica Pura e Aplicada (IMPA)"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zoraida F.","family":"Rico","sequence":"additional","affiliation":[{"name":"Department of Statistics, Columbia University"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"108","reference":[{"key":"18","doi-asserted-by":"publisher","unstructured":"Ledoux, M.<\/small> (2001). 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