Improved Concentration for Mean Estimators via Shrinkage
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908714292740096 |
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| author | Catão, Antônio Resende, Lucas Orenstein, Paulo |
| author_facet | Catão, Antônio Resende, Lucas Orenstein, Paulo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_12750 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Improved Concentration for Mean Estimators via Shrinkage Catão, Antônio Resende, Lucas Orenstein, Paulo Statistics Theory 62G35, 62F35 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. |
| title | Improved Concentration for Mean Estimators via Shrinkage |
| topic | Statistics Theory 62G35, 62F35 |
| url | https://arxiv.org/abs/2512.12750 |