# Statistical Inference and Large-scale Multiple Testing for High-dimensional Regression Models

arXiv: https://arxiv.org/abs/2301.10392 · HTML: https://mlsanity.com/paper/2301.10392/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jan 2023.

## Built on by (most cited first, 4 of 4)

- [Interval Estimation of Coefficients in Penalized Regression Models of Insurance Data](https://mlsanity.com/paper/2410.01008/) (2024)
- [Statistical Inference for Linear Functionals of Online SGD in High-dimensional Linear Regression](https://mlsanity.com/paper/2302.09727/) (2023)
- [Statistical Inference for Linear Functionals of Online Least-squares SGD when t gtrsim d1+δ](https://mlsanity.com/paper/2510.19734/) (2025)
- [Recovering linear images of sparse signals from indirect observations](https://mlsanity.com/paper/2609.06182/) (2026)

## Abstract (arXiv)

This paper presents a selective survey of recent developments in statistical inference and multiple testing for high-dimensional regression models, including linear and logistic regression. We examine the construction of confidence intervals and hypothesis tests for various low-dimensional objectives such as regression coefficients and linear and quadratic functionals. The key technique is to generate debiased and desparsified estimators for the targeted low-dimensional objectives and estimate their uncertainty. In addition to covering the motivations for and intuitions behind these statistical methods, we also discuss their optimality and adaptivity in the context of high-dimensional inference. In addition, we review the recent development of statistical inference based on multiple regression models and the advancement of large-scale multiple testing for high-dimensional regression. The R package SIHR has implemented some of the high-dimensional inference methods discussed in this paper.