{"paper":{"title":"Detection of a sparse submatrix of a high-dimensional noisy matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Cristina Butucea, Yuri I. Ingster","submitted_at":"2011-09-05T13:40:37Z","abstract_excerpt":"We observe a $N\\times M$ matrix $Y_{ij}=s_{ij}+\\xi_{ij}$ with $\\xi_{ij}\\sim {\\mathcal {N}}(0,1)$ i.i.d. in $i,j$, and $s_{ij}\\in \\mathbb {R}$. We test the null hypothesis $s_{ij}=0$ for all $i,j$ against the alternative that there exists some submatrix of size $n\\times m$ with significant elements in the sense that $s_{ij}\\ge a>0$. We propose a test procedure and compute the asymptotical detection boundary $a$ so that the maximal testing risk tends to 0 as $M\\to\\infty$, $N\\to\\infty$, $p=n/N\\to0$, $q=m/M\\to0$. We prove that this boundary is asymptotically sharp minimax under some additional con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.0898","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"}