{"paper":{"title":"Admissible Bayes equivariant estimation of location vectors for spherically symmetric distributions with unknown scale","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"William E. Strawderman, Yuzo Maruyama","submitted_at":"2017-10-08T07:26:24Z","abstract_excerpt":"This paper investigates estimation of the mean vector under invariant quadratic loss for a spherically symmetric location family with a residual vector with density of the form $ f(x,u)=\\eta^{(p+n)/2}f(\\eta\\{\\|x-\\theta\\|^2+\\|u\\|^2\\}) $, where $\\eta$ is unknown. We show that the natural estimator $x$ is admissible for $p=1,2$. Also, for $p\\geq 3$, we find classes of generalized Bayes estimators that are admissible within the class of equivariant estimators of the form $\\{1-\\xi(x/\\|u\\|)\\}x$. In the Gaussian case, a variant of the James--Stein estimator, $[1-\\{(p-2)/(n+2)\\}/\\{\\|x\\|^2/\\|u\\|^2+(p-2"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.02794","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"}