{"paper":{"title":"Inference for a constrained parameter in presence of an uncertain constraint","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"\\'Eric Marchand, Theodoros Nicoleris","submitted_at":"2018-06-07T10:04:11Z","abstract_excerpt":"We describe a hierarchical Bayesian approach for inference about a parameter $\\theta$ lower-bounded by $\\alpha$ with uncertain $\\alpha$, derive some basic identities for posterior analysis about $(\\theta,\\alpha)$, and provide illustrations for normal and Poisson models. For the normal case with unknown mean $\\theta$ and known variance $\\sigma^2$, we obtain Bayes estimators of $\\theta$ that take values on $\\mathbb{R}$, but that are equally adapted to a lower-bound constraint in being minimax under squared error loss for the constrained problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.02594","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"}