{"paper":{"title":"A note on the approximate admissibility of regularized estimators in the Gaussian sequence model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Adityanand Guntuboyina, Xi Chen, Yuchen Zhang","submitted_at":"2017-03-01T23:08:33Z","abstract_excerpt":"We study the problem of estimating an unknown vector $\\theta$ from an observation $X$ drawn according to the normal distribution with mean $\\theta$ and identity covariance matrix under the knowledge that $\\theta$ belongs to a known closed convex set $\\Theta$. In this general setting, Chatterjee (2014) proved that the natural constrained least squares estimator is \"approximately admissible\" for every $\\Theta$. We extend this result by proving that the same property holds for all convex penalized estimators as well. Moreover, we simplify and shorten the original proof considerably. We also provi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.00542","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"}