{"paper":{"title":"Multidimensional two-component Gaussian mixtures detection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"B\\'eatrice Laurent (IMT), Cathy Maugis-Rabusseau (IMT), Cl\\'ement Marteau (IMT)","submitted_at":"2015-09-30T11:38:07Z","abstract_excerpt":"Let $(X\\_1,\\ldots,X\\_n)$ be a $d$-dimensional i.i.d sample from a distribution with density $f$. The problem of detection of a two-component mixture is considered. Our aim is to decide whether $f$ is the density of a standard Gaussian random $d$-vector ($f=\\phi\\_d$) against $f$ is a two-component mixture: $f=(1-\\varepsilon)\\phi\\_d +\\varepsilon \\phi\\_d (.-\\mu)$ where $(\\varepsilon,\\mu)$ are  unknown parameters. Optimal separation conditions on $\\varepsilon, \\mu, n$ and the dimension $d$ are established, allowing to separate both hypotheses with prescribed errors. Several testing procedures are "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.09129","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"}