# Robust Inference for High-Dimensional Linear Models via Residual Randomization

arXiv: https://arxiv.org/abs/2106.07717 · HTML: https://mlsanity.com/paper/2106.07717/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 30 references that are in the map.
- First posted on arXiv 14 Jun 2021.

## Builds on (most cited first, 6 of 6)

- [Confidence Intervals and Hypothesis Testing for High-Dimensional Regression](https://mlsanity.com/paper/1306.3171/) (2013)
- [Moving Beyond Sub-Gaussianity in High-Dimensional Statistics: Applications in Covariance Estimation and Linear Regression](https://mlsanity.com/paper/1804.02605/) (2018)
- [High-dimensional simultaneous inference with the bootstrap](https://mlsanity.com/paper/1606.03940/) (2016)
- [Inference in High Dimensional Panel Models with an Application to Gun Control](https://mlsanity.com/paper/1411.6507/) (2014)
- [A Bootstrap Lasso + Partial Ridge Method to Construct Confidence Intervals for Parameters in High-dimensional Sparse Linear Models](https://mlsanity.com/paper/1706.02150/) (2017)
- [A Residual Bootstrap for High-Dimensional Regression with Near Low-Rank Designs](https://mlsanity.com/paper/1607.00743/) (2016)

## Abstract (arXiv)

We propose a residual randomization procedure designed for robust Lasso-based inference in the high-dimensional setting. Compared to earlier work that focuses on sub-Gaussian errors, the proposed procedure is designed to work robustly in settings that also include heavy-tailed covariates and errors. Moreover, our procedure can be valid under clustered errors, which is important in practice, but has been largely overlooked by earlier work. Through extensive simulations, we illustrate our method's wider range of applicability as suggested by theory. In particular, we show that our method outperforms state-of-art methods in challenging, yet more realistic, settings where the distribution of covariates is heavy-tailed or the sample size is small, while it remains competitive in standard, "well behaved" settings previously studied in the literature.