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)|
|Title of host publication||Proceedings of Advances in Neural Information Processing Systems 30 (NIPS 2017)|
|Editors||Isabelle Guyon, Ulrike Von Von Luxburg, Samy Bengio|
|State||Published - 2017|