{"ID":2829348,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.12750","arxiv_id":"2512.12750","title":"Improved Concentration for Mean Estimators via Shrinkage","abstract":"We study a class of robust mean estimators $\\widehatμ$ obtained by adaptively shrinking the weights of sample points far from a base estimator $\\widehatκ$. Given a data-dependent scaling factor $\\widehatα$ and a weighting function $w:[0, \\infty) \\to [0,1]$, we let $\\widehatμ = \\widehatκ + \\frac{1}{n}\\sum_{i=1}^n(X_i - \\widehatκ)w(\\widehatα|X_i-\\widehatκ|) $. We prove that, under mild assumptions over $w$, these estimators achieve stronger concentration bounds than the base estimate $\\widehatκ$, including sub-Gaussian guarantees. This framework unifies and extends several existing approaches to robust mean estimation in $\\mathbb{R}$. Through numerical experiments, we show that our shrinking approach translates to faster concentration, even for small sample sizes.","short_abstract":"We study a class of robust mean estimators $\\widehatμ$ obtained by adaptively shrinking the weights of sample points far from a base estimator $\\widehatκ$. Given a data-dependent scaling factor $\\widehatα$ and a weighting function $w:[0, \\infty) \\to [0,1]$, we let $\\widehatμ = \\widehatκ + \\frac{1}{n}\\sum_{i=1}^n(X_i -...","url_abs":"https://arxiv.org/abs/2512.12750","url_pdf":"https://arxiv.org/pdf/2512.12750v2","authors":"[\"Antônio Catão\",\"Lucas Resende\",\"Paulo Orenstein\"]","published":"2025-12-14T16:18:22Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[]","has_code":false}