{"paper":{"title":"Sharp detection of smooth signals in a high-dimensional sparse matrix with indirect observations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Cristina Butucea, Ghislaine Gayraud","submitted_at":"2013-01-20T14:14:27Z","abstract_excerpt":"We consider a matrix-valued Gaussian sequence model, that is, we observe a sequence of high-dimensional $M \\times N$ matrices of heterogeneous Gaussian random variables $x_{ij,k}$ for $i \\in\\{1,...,M\\}$, $j \\in \\{1,...,N\\}$ and $k \\in \\mathbb{Z}$. The standard deviation of our observations is $\\ep k^s$ for some $\\ep >0$ and $s \\geq 0$.\n  We give sharp rates for the detection of a sparse submatrix of size $m \\times n$ with active components. A component $(i,j)$ is said active if the sequence $\\{x_{ij,k}\\}_k$ have mean $\\{\\theta_{ij,k}\\}_k$ within a Sobolev ellipsoid of smoothness $\\tau >0$ and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.4660","kind":"arxiv","version":1},"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"}