{"paper":{"title":"Contribution to the theory of Pitman estimators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Abram M. Kagan, Andrew Barron, Mokshay Madiman, Tinghui Yu","submitted_at":"2013-02-13T21:09:17Z","abstract_excerpt":"New inequalities are proved for the variance of the Pitman estimators (minimum variance equivariant estimators) of \\theta constructed from samples of fixed size from populations F(x-\\theta). The inequalities are closely related to the classical Stam inequality for the Fisher information, its analog in small samples, and a powerful variance drop inequality. The only condition required is finite variance of F; even the absolute continuity of F is not assumed. As corollaries of the main inequalities for small samples, one obtains alternate proofs of known properties of the Fisher information, as "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.3238","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"}