# High-Dimensional Single-Index Models: Link Estimation and Marginal Inference

arXiv: https://arxiv.org/abs/2404.17812 · HTML: https://mlsanity.com/paper/2404.17812/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Apr 2024.

## Built on by (most cited first, 1 of 1)

- [Provable FDR Control for Deep Feature Selection: Deep MLPs and Beyond](https://mlsanity.com/paper/2512.04696/) (2025)

## Abstract (arXiv)

This study proposes a novel method for estimation and hypothesis testing in high-dimensional single-index models. We address a common scenario where the sample size and the dimension of regression coefficients are large and comparable. Unlike previous approaches, which often overlook the estimation of the unknown link function, we introduce a new method for link function estimation. Leveraging the information from the estimated link function, we propose more efficient estimators that are better aligned with the underlying model. Furthermore, we rigorously establish the asymptotic normality of each coordinate of the estimator. This provides a valid construction of confidence intervals and p-values for any finite collection of coordinates. Numerical experiments validate our theoretical results.