# Robust Inference via Multiplier Bootstrap

## TL;DR

This paper develops a robust inference method using multiplier bootstrap combined with adaptive Huber regression, effectively handling heavy-tailed data in confidence set construction and hypothesis testing, outperforming traditional least squares approaches.

## Contribution

It introduces a novel robust inference framework that integrates adaptive Huber regression with multiplier bootstrap, addressing heavy-tailed data challenges.

## Key findings

- The proposed method improves finite sample properties over least squares.
- It provides reliable confidence sets and hypothesis tests under heavy-tailed noise.
- Empirical results confirm the theoretical advantages of the approach.

## Abstract

This paper investigates the theoretical underpinnings of two fundamental statistical inference problems, the construction of confidence sets and large-scale simultaneous hypothesis testing, in the presence of heavy-tailed data. With heavy-tailed observation noise, finite sample properties of the least squares-based methods, typified by the sample mean, are suboptimal both theoretically and empirically. In this paper, we demonstrate that the adaptive Huber regression, integrated with the multiplier bootstrap procedure, provides a useful robust alternative to the method of least squares. Our theoretical and empirical results reveal the effectiveness of the proposed method, and highlight the importance of having inference methods that are robust to heavy tailedness.