Estimating High-dimensional Non-Gaussian Multiple Index Models via Stein’s Lemma

Zhuoran Yang, Krishnakumar Balasubramanian, Zhaoran Wang, Han Liu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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.
Original languageEnglish (US)
Title of host publicationProceedings of Advances in Neural Information Processing Systems 30 (NIPS 2017)
EditorsIsabelle Guyon, Ulrike Von Von Luxburg, Samy Bengio
StatePublished - 2017

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