{"paper":{"title":"Sparse single-index model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"CREST), DMA), G\\'erard Biau (LPMA, LSTA, Pierre Alquier (LPMA","submitted_at":"2011-01-17T14:36:55Z","abstract_excerpt":"Let $(\\bX, Y)$ be a random pair taking values in $\\mathbb R^p \\times \\mathbb R$. In the so-called single-index model, one has $Y=f^{\\star}(\\theta^{\\star T}\\bX)+\\bW$, where $f^{\\star}$ is an unknown univariate measurable function, $\\theta^{\\star}$ is an unknown vector in $\\mathbb R^d$, and $W$ denotes a random noise satisfying $\\mathbb E[\\bW|\\bX]=0$. The single-index model is known to offer a flexible way to model a variety of high-dimensional real-world phenomena. However, despite its relative simplicity, this dimension reduction scheme is faced with severe complications as soon as the underly"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3229","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"}