{"paper":{"title":"A Neighborhood-Assisted Hotelling's $T^2$ Test for High-Dimensional Means","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Jun Li, Lingjun Li, Yumou Qiu","submitted_at":"2017-12-05T18:24:16Z","abstract_excerpt":"Many tests have been proposed to remedy the classical Hotelling's $T^2$ test in the \"large $p$, small $n$\" paradigm, but the existence of an optimal sum-of-squares type test has not been explored. This paper shows that under certain conditions, the population Hotelling's $T^2$ test with the known $\\Sigma^{-1}$ attains the best power among all the $L_2$-norm based tests with the data transformation by $\\Sigma^{\\eta}$ for $\\eta \\in (-\\infty, \\infty)$. To extend the result to the case of unknown $\\Sigma^{-1}$, we propose a Neighborhood-Assisted Hotelling's $T^2$ statistic obtained by replacing th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.01798","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"}