发表机构
Baruch College; Yale University（巴鲁克学院; 耶鲁大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
HOMER通过径向Huber中心聚合块均值，在希尔伯特空间中实现高效鲁棒估计，重尾场景下稳定，高斯场景接近经验均值效率，但受多数块污染时会失效。
AI 中文摘要
重尾分布会削弱经验均值的高置信度控制，几何均值聚合（MOM）也缺乏向均值效率靠拢的阈值。我们提出HOMER，即高效鲁棒估计的Huber均值聚合方法，它通过径向Huber中心聚合块均值。其标准形式和伪Huber形式对每个块得分进行约束，在类中位数鲁棒性与经验均值之间插值。我们建立了希尔伯特空间多数定理和有限二阶矩下的MOM阶偏差界：标准HOMER在二次区域内退化为样本均值；伪HOMER随阈值增大趋近样本均值，还具有渐近线性性，能对总体块Huber目标进行一致的三明治协方差估计。在有限三阶矩下，固定有限维投影以常规参数速率支持均值推断，该结果要求块大小和块数量增长，且块大小增长更快。重尾模拟显示，当少数块摘要被偏移时，HOMER保持稳定；在干净高斯数据上，两种形式均接近经验均值的效率。有限块三明治区间覆盖不足，尤其针对偏斜函数数据；进一步研究表明，当污染影响多数块或破坏普通块内均值时，HOMER会失效。
英文摘要
Heavy tails weaken high-confidence control for the empirical mean. Geometric median-of-means (MOM) also lacks a threshold that moves toward mean efficiency. We propose \emph{HOMER}, or Huber-of-Means for Efficient and Robust Estimation. HOMER aggregates block means through a radial Huber center. Its canonical and pseudo-Huber forms bound each block score and interpolate between median-like robustness and the empirical mean. We establish a Hilbert-space majority theorem and a MOM-order deviation bound under a finite second moment. Canonical HOMER recovers the sample mean inside its quadratic region. Pseudo-HOMER approaches the sample mean as the threshold grows. It also admits asymptotic linearity and consistent sandwich covariance estimation around the population block-Huber target. Under a finite third moment, fixed finite-dimensional projections support mean inference at the usual parametric rate. This result requires growing block sizes and counts, with block sizes increasing faster. Heavy-tailed simulations show that HOMER remains stable when a minority of block summaries is displaced. On clean Gaussian data, both versions closely approach the empirical mean's efficiency. Finite-block sandwich intervals undercovered, especially for skewed functional data. Further studies show failure when contamination affects most blocks or compromises ordinary within-block means.
