{"paper":{"title":"Improved Concentration for Mean Estimators via Shrinkage","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Ant\\^onio Cat\\~ao, Lucas Resende, Paulo Orenstein","submitted_at":"2025-12-14T16:18:22Z","abstract_excerpt":"We study a class of robust mean estimators $\\widehat{\\mu}$ obtained by adaptively shrinking the weights of sample points far from a base estimator $\\widehat{\\kappa}$. Given a data-dependent scaling factor $\\widehat{\\alpha}$ and a weighting function $w:[0, \\infty) \\to [0,1]$, we let $\\widehat{\\mu}=\\widehat{\\kappa} + \\frac{1}{n}\\sum_{i=1}^n(X_i - \\widehat{\\kappa})w(\\widehat{\\alpha}|X_i-\\widehat{\\kappa}|)$. We prove that, under mild assumptions over $w$, these estimators achieve stronger concentration bounds than the base estimate $\\widehat{\\kappa}$, including sub-Gaussian guarantees. This framew"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.12750","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2512.12750/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}