{"paper":{"title":"On the optimality of sliced inverse regression in high dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Dongming Huang, Jun S. Liu, Qian Lin, Xinran Li","submitted_at":"2017-01-21T11:08:12Z","abstract_excerpt":"The central subspace of a pair of random variables $(y,x) \\in \\mathbb{R}^{p+1}$ is the minimal subspace $\\mathcal{S}$ such that $y \\perp \\hspace{-2mm} \\perp x\\mid P_{\\mathcal{S}}x$. In this paper, we consider the minimax rate of estimating the central space of the multiple index models $y=f(\\beta_{1}^{\\tau}x,\\beta_{2}^{\\tau}x,...,\\beta_{d}^{\\tau}x,\\epsilon)$ with at most $s$ active predictors where $x \\sim N(0,I_{p})$. We first introduce a large class of models depending on the smallest non-zero eigenvalue $\\lambda$ of $var(\\mathbb{E}[x|y])$, over which we show that an aggregated estimator bas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06009","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"}