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

Part of Advances in Neural Information Processing Systems 30 (NIPS 2017)

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Authors

Zhuoran Yang, Krishnakumar Balasubramanian, Zhaoran Wang, Han Liu

Abstract

<p>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.</p>