# Robust Inference via Multiplier Bootstrap

arXiv: https://arxiv.org/abs/1903.07208 · HTML: https://mlsanity.com/paper/1903.07208/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Mar 2019.

## Built on by (most cited first, 8 of 8)

- [Robust and Sparse Estimation of Linear Regression Coefficients with Heavy-tailed Noises and Covariates](https://mlsanity.com/paper/2206.07594/) (2022)
- [Outlier Robust and Sparse Estimation of Linear Regression Coefficients](https://mlsanity.com/paper/2208.11592/) (2022)
- [Confidence Sets under Generalized Self-Concordance](https://mlsanity.com/paper/2301.00260/) (2022)
- [Probabilistic Modeling of Disparity Uncertainty for Robust and Efficient Stereo Matching](https://mlsanity.com/paper/2412.18703/) (2024)
- [Adversarial robust weighted Huber regression](https://mlsanity.com/paper/2102.11120/) (2021)
- [Robust High-dimensional Tuning Free Multiple Testing](https://mlsanity.com/paper/2211.11959/) (2022)
- [Estimation of sparse linear regression coefficients under L-subexponential covariates](https://mlsanity.com/paper/2304.11958/) (2023)
- [Sparse Linear Regression when Noises and Covariates are Heavy-Tailed and Contaminated by Outliers](https://mlsanity.com/paper/2408.01336/) (2024)

## Abstract (arXiv)

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.