Estimating High-Dimensional Non-Gaussian Multiple Index Models via Stein’s Lemma
Abstract
We consider estimating the parametric components of semiparametric multi-index models in high dimensions. To bypass the requirements of Gaussianity or elliptical symmetry of covariates in existing methods, we propose to leverage a second-order Stein’s method with score function-based corrections. We prove that our estimator achieves a near-optimal statistical rate of convergence even when the score function or the response variable is heavy-tailed. To establish the key concentration results, we develop a data-driven truncation argument that may be of independent interest. We supplement our theoretical findings with simulations.
Cite
Text
Yang et al. "Estimating High-Dimensional Non-Gaussian Multiple Index Models via Stein’s Lemma." Neural Information Processing Systems, 2017.Markdown
[Yang et al. "Estimating High-Dimensional Non-Gaussian Multiple Index Models via Stein’s Lemma." Neural Information Processing Systems, 2017.](https://mlanthology.org/neurips/2017/yang2017neurips-estimating/)BibTeX
@inproceedings{yang2017neurips-estimating,
title = {{Estimating High-Dimensional Non-Gaussian Multiple Index Models via Stein’s Lemma}},
author = {Yang, Zhuoran and Balasubramanian, Krishnakumar and Wang, Zhaoran and Liu, Han},
booktitle = {Neural Information Processing Systems},
year = {2017},
pages = {6097-6106},
url = {https://mlanthology.org/neurips/2017/yang2017neurips-estimating/}
}