{"paper":{"title":"Shrinkage Estimation in Multilevel Normal Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Carl N. Morris, Martin Lysy","submitted_at":"2012-03-26T09:38:12Z","abstract_excerpt":"This review traces the evolution of theory that started when Charles Stein in 1955 [In Proc. 3rd Berkeley Sympos. Math. Statist. Probab. I (1956) 197--206, Univ. California Press] showed that using each separate sample mean from $k\\ge3$ Normal populations to estimate its own population mean $\\mu_i$ can be improved upon uniformly for every possible $\\mu=(\\mu_1,...,\\mu_k)'$. The dominating estimators, referred to here as being \"Model-I minimax,\" can be found by shrinking the sample means toward any constant vector. Admissible minimax shrinkage estimators were derived by Stein and others as poste"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.5610","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"}