{"paper":{"title":"Sufficient dimension reduction with additional information","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Chih-Yen Liu, Henry Horng-Shing Lu, Hung Hung","submitted_at":"2014-10-14T03:44:35Z","abstract_excerpt":"Sufficient dimension reduction is widely applied to help model building between the response $Y$ and covariate $X$. While the target of interest is the relationship between $(Y,X)$, in some applications we also collect additional variable $W$ that is strongly correlated with $Y$. From a statistical point of view, making inference about $(Y,X)$ without using $W$ will lose efficiency. However, it is not trivial to incorporate the information of $W$ to infer $(Y,X)$. In this article, we propose a two-stage dimension reduction method for $(Y,X)$, that is able to utilize the additional information "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3561","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"}