# High-dimensional simultaneous inference with the bootstrap

arXiv: https://arxiv.org/abs/1606.03940 · HTML: https://mlsanity.com/paper/1606.03940/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jun 2016.

## Built on by (most cited first, 9 of 9)

- [Are Latent Factor Regression and Sparse Regression Adequate?](https://mlsanity.com/paper/2203.01219/) (2022)
- [Distributed Bootstrap for Simultaneous Inference Under High Dimensionality](https://mlsanity.com/paper/2102.10080/) (2021)
- [Correcting Confounding via Random Selection of Background Variables](https://mlsanity.com/paper/2202.02150/) (2022)
- [Spatially relaxed inference on high-dimensional linear models](https://mlsanity.com/paper/2106.02590/) (2021)
- [Robust Inference for High-Dimensional Linear Models via Residual Randomization](https://mlsanity.com/paper/2106.07717/) (2021)
- [Sparsified Simultaneous Confidence Intervals for High-Dimensional Linear Models](https://mlsanity.com/paper/2307.07574/) (2023)
- [Inference with non-differentiable surrogate loss in a general high-dimensional classification framework](https://mlsanity.com/paper/2405.11723/) (2024)
- [Learning Centre Partitions from Summaries](https://mlsanity.com/paper/2509.16337/) (2025)
- [Recovering linear images of sparse signals from indirect observations](https://mlsanity.com/paper/2609.06182/) (2026)

## Abstract (arXiv)

We propose a residual and wild bootstrap methodology for individual and simultaneous inference in high-dimensional linear models with possibly non-Gaussian and heteroscedastic errors. We establish asymptotic consistency for simultaneous inference for parameters in groups G, where p gg n, s0 = o(n1/2/log(p) log(|G|)1/2) and log(|G|) = o(n1/7), with p the number of variables, n the sample size and s0 denoting the sparsity. The theory is complemented by many empirical results. Our proposed procedures are implemented in the R-package hdi.