{"paper":{"title":"Global testing under the sparse alternatives for single index models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Jun S. Liu, Qian Lin, Zhigen Zhao","submitted_at":"2018-05-04T15:21:59Z","abstract_excerpt":"For the single index model $y=f(\\beta^{\\tau}x,\\epsilon)$ with Gaussian design, %satisfying that rank $var(\\mathbb{E}[x\\mid y])=1$ where $f$ is unknown and $\\beta$ is a sparse $p$-dimensional unit vector with at most $s$ nonzero entries, we are interested in testing the null hypothesis that $\\beta$, when viewed as a whole vector, is zero against the alternative that some entries of $\\beta$ is nonzero. Assuming that $var(\\mathbb{E}[x \\mid y])$ is non-vanishing, we define the generalized signal-to-noise ratio (gSNR) $\\lambda$ of the model as the unique non-zero eigenvalue of $var(\\mathbb{E}[x \\mi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.01820","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"}