{"paper":{"title":"On efficient prediction and predictive density estimation for spherically symmetric models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Dominique Fourdrinier, \\'Eric Marchand, William E. Strawderman","submitted_at":"2018-07-12T16:28:37Z","abstract_excerpt":"Let $X,U,Y$ be spherically symmetric distributed having density $$\\eta^{d +k/2} \\, f\\left(\\eta(\\|x-\\theta|^2+ \\|u\\|^2 + \\|y-c\\theta\\|^2 ) \\right)\\,,$$ with unknown parameters $\\theta \\in \\mathbb{R}^d$ and $\\eta>0$, and with known density $f$ and constant $c >0$. Based on observing $X=x,U=u$, we consider the problem of obtaining a predictive density $\\hat{q}(y;x,u)$ for $Y$ as measured by the expected Kullback-Leibler loss. A benchmark procedure is the minimum risk equivariant density $\\hat{q}_{mre}$, which is Generalized Bayes with respect to the prior $\\pi(\\theta, \\eta) = \\eta^{-1}$. For $d \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.04711","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"}