Efficient median of means estimator

TL;DR

This paper introduces a modified median of means estimator that achieves near-optimal sub-Gaussian deviation bounds with minimal assumptions, improving robustness and efficiency in statistical estimation.

Contribution

The paper proposes a new variant of the median of means estimator that requires weaker assumptions and provides nearly optimal deviation bounds.

Findings

Achieves sub-Gaussian deviation bounds with minimal assumptions

Requires weaker distributional assumptions than previous methods

Provides nearly optimal constants in deviation bounds

Abstract

The goal of this note is to present a modification of the popular median of means estimator that achieves sub-Gaussian deviation bounds with nearly optimal constants under minimal assumptions on the underlying distribution. We build on a recent work on the topic by the author, and prove that desired guarantees can be attained under weaker requirements.