HOMER: Huber-of-Means for Efficient and Robust Estimation in Hilbert Spaces
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 l...
| Authors | Kisung You, Boram Cho |
|---|---|
| Primary category | stat.ML |
| Published | 29 July 2026 |
| Last updated at source | 29 July 2026 |
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