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 language | English (US) |
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Pages (from-to) | 6098-6107 |
Number of pages | 10 |
Journal | Advances in Neural Information Processing Systems |
Volume | 2017-December |
State | Published - 2017 |
Event | 31st Annual Conference on Neural Information Processing Systems, NIPS 2017 - Long Beach, United States Duration: Dec 4 2017 → Dec 9 2017 |
ASJC Scopus subject areas
- Computer Networks and Communications
- Information Systems
- Signal Processing