{"paper":{"title":"Adaptive estimation in the nonparametric random coefficients binary choice model by needlet thresholding","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Eric Gautier (TSE), Erwan Le Pennec (CMAP, XPOP)","submitted_at":"2011-06-17T14:51:11Z","abstract_excerpt":"In the random coefficients binary choice model, a binary variable equals 1 iff an index $X^\\top\\beta$  is positive.The vectors $X$ and $\\beta$ are independent and belong to the sphere $\\mathbb{S}^{d-1}$ in $\\mathbb{R}^{d}$.We prove lower bounds on the minimax risk for estimation of the density $f\\_{\\beta}$ over Besov bodies where the loss is a power of the $L^p(\\mathbb{S}^{d-1})$ norm for $1\\le p\\le \\infty$.  We show that a hard thresholding estimator based on a needlet expansion with data-driven thresholds achieves these lower bounds up to logarithmic factors."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.3503","kind":"arxiv","version":3},"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"}