{"paper":{"title":"Estimation of a multivariate normal mean with a bounded signal to noise ratio","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"\\'Eric Marchand, Othmane Kortbi","submitted_at":"2012-04-26T20:28:18Z","abstract_excerpt":"For normal canonical models with $X \\sim N_p(\\theta, \\sigma^{2} I_{p}), \\;\\; S^{2} \\sim \\sigma^{2}\\chi^{2}_{k}, \\;{independent}$, we consider the problem of estimating $\\theta$ under scale invariant squared error loss $\\frac{\\|d-\\theta \\|^{2}}{\\sigma^{2}}$, when it is known that the signal-to-noise ratio $\\frac{\\|\\theta\\|}{\\sigma}$ is bounded above by $m$. Risk analysis is achieved by making use of a conditional risk decomposition and we obtain in particular sufficient conditions for an estimator to dominate either the unbiased estimator $\\delta_{UB}(X)=X$, or the maximum likelihood estimator "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.6054","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"}