# On Stein's Identity and Near-Optimal Estimation in High-dimensional Index Models

arXiv: https://arxiv.org/abs/1709.08795 · HTML: https://mlsanity.com/paper/1709.08795/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Sep 2017.

## Built on by (most cited first, 2 of 2)

- [Dimension Reduction and MARS](https://mlsanity.com/paper/2302.05790/) (2023)
- [Low-Rank Single-Index Bandits with Unknown Links: From Matrices to Tensors](https://mlsanity.com/paper/2609.33025/) (2026)

## Abstract (arXiv)

We consider estimating the parametric components of semi-parametric multiple index models in a high-dimensional and non-Gaussian setting. Such models form a rich class of non-linear models with applications to signal processing, machine learning and statistics. Our estimators leverage the score function based first and second-order Stein's identities and do not require the covariates to satisfy Gaussian or elliptical symmetry assumptions common in the literature. Moreover, to handle score functions and responses that are heavy-tailed, our estimators are constructed via carefully thresholding their empirical counterparts. We show that our estimator achieves near-optimal statistical rate of convergence in several settings. We supplement our theoretical results via simulation experiments that confirm the theory.