{"paper":{"title":"Improved Inference on the Rank of a Matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.ME","stat.TH"],"primary_cat":"econ.EM","authors_text":"Qihui Chen, Zheng Fang","submitted_at":"2018-12-06T03:46:11Z","abstract_excerpt":"This paper develops a general framework for conducting inference on the rank of an unknown matrix $\\Pi_0$. A defining feature of our setup is the null hypothesis of the form $\\mathrm H_0: \\mathrm{rank}(\\Pi_0)\\le r$. The problem is of first order importance because the previous literature focuses on $\\mathrm H_0': \\mathrm{rank}(\\Pi_0)= r$ by implicitly assuming away $\\mathrm{rank}(\\Pi_0)<r$, which may lead to invalid rank tests due to over-rejections. In particular, we show that limiting distributions of test statistics under $\\mathrm H_0'$ may not stochastically dominate those under $\\mathrm{r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.02337","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"}