Do we need to estimate the variance in robust mean estimation?

TMLR Paper1503 Authors

Abstract:

In this paper, we propose self-tuned robust estimators for estimating the mean of heavy-tailed distributions, where heavy-tailed distributions refer to distributions with only finite variances.
Our method involves introducing a new loss function that considers both the mean parameter and a robustification parameter. By simultaneously optimizing the empirical loss function with respect to both parameters, the resulting estimator for the robustification parameter {can automatically adapt to the unknown data variance and can achieve near-optimal finite-sample performance.} Our approach outperforms previous methods in terms of both computational and asymptotic efficiency. Specifically, it does not require cross-validation or Lepski's method to tune the robustification parameter, and the variance of our estimator achieves the Cram\'er-Rao lower bound.

Submission Length: Long submission (more than 12 pages of main content)

Previous TMLR Submission Url: https://openreview.net/forum?id=NGa8UryQ2F

Changes Since Last Submission: revision

Assigned Action Editor: ~Pierre_Alquier1

Submission Number: 1503