{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T18:00:29Z","timestamp":1791396029690,"version":"4.3.3"},"reference-count":45,"publisher":"Institute of Mathematical Statistics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Ann. Statist."],"published-print":{"date-parts":[[2024,8,1]]},"abstract":"This work investigates multiple testing by considering minimax separation rates in the sparse sequence model, when the testing risk is measured as the sum FDR+FNR (False Discovery Rate plus False Negative Rate). First, using the popular beta-min separation condition, with all nonzero signals separated from 0 by at least some amount, we determine the sharp minimax testing risk asymptotically and thereby explicitly describe the transition from \u201cachievable multiple testing with vanishing risk\u201d to \u201cimpossible multiple testing.\u201d Adaptive multiple testing procedures achieving the corresponding optimal boundary are provided: the Benjamini\u2013Hochberg procedure with a properly tuned level, and an empirical Bayes \u2113-value (\u2018local FDR\u2019) procedure. We prove that the FDR and FNR make nonsymmetric contributions to the testing risk for most optimal procedures, the FNR part being dominant at the boundary. The multiple testing hardness is then investigated for classes of arbitrary sparse signals. A number of extensions, including results for classification losses and convergence rates in the case of large signals, are also investigated.<\/jats:p>","DOI":"10.1214\/24-aos2404","type":"journal-article","created":{"date-parts":[[2024,10,4]],"date-time":"2024-10-04T01:50:27Z","timestamp":1728006627000},"page":"1564-1591","source":"Crossref","is-referenced-by-count":7,"title":["Sharp multiple testing boundary for sparse sequences"],"prefix":"10.1214","volume":"52","author":[{"given":"Kweku","family":"Abraham","sequence":"first","affiliation":[{"name":"Department of Pure Mathematics and Mathematical Statistics, University of Cambridge"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Isma\u00ebl","family":"Castillo","sequence":"additional","affiliation":[{"name":"Laboratoire de Probabilit\u00e9s, Statistique et Mod\u00e9lisation (LPSM), Sorbonne Universit\u00e9"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"\u00c9tienne","family":"Roquain","sequence":"additional","affiliation":[{"name":"Laboratoire de Probabilit\u00e9s, Statistique et Mod\u00e9lisation (LPSM), Sorbonne Universit\u00e9"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"108","reference":[{"key":"31","doi-asserted-by":"publisher","unstructured":"Ingster, Y. 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