{"paper":{"title":"On shrinkage estimation for balanced loss functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"\\'Eric Marchand, William E. Strawderman","submitted_at":"2019-04-05T17:39:16Z","abstract_excerpt":"The estimation of a multivariate mean $\\theta$ is considered under natural modifications of balanced loss function of the form: (i) $\\omega \\, \\rho(\\|\\delta-\\delta_0\\|^2) + (1-\\omega) \\, \\rho(\\|\\delta-\\theta\\|^2) $, and (ii) $\\ell \\left( \\omega \\, \\|\\delta-\\delta_0\\|^2 + (1-\\omega) \\, \\|\\delta-\\theta\\|^2 \\right)\\,$, where $\\delta_0$ is a target estimator of $\\gamma(\\theta)$. After briefly reviewing known results for original balanced loss with identity $\\rho$ or $\\ell$, we provide, for increasing and concave $\\rho$ and $\\ell$ which also satisfy a completely monotone property, Baranchik-type es"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.03171","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"}