High-dimensional non-Gaussian single index models via thresholded score function estimation

Zhuoran Yang, Krishnakumar Balasubramanian, Han Liu*

*Corresponding author for this work

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

1 Scopus citations

Abstract

We consider estimating the parametric component of single index models in high dimensions. Compared with existing work, we do not require the covariate to be normally distributed. Utilizing Stein's Lemma, we propose estimators based on the score function of the covariate. Moreover, to handle score function and response variables that are heavy-tailed, our estimators are constructed via carefully thresholding their empirical counterparts. Under a bounded fourth moment condition, we establish optimal statistical rates of convergence for the proposed estimators. Extensive numerical experiments are provided to back up our theory.

Original languageEnglish (US)
Title of host publication34th International Conference on Machine Learning, ICML 2017
PublisherInternational Machine Learning Society (IMLS)
Pages5878-5887
Number of pages10
ISBN (Electronic)9781510855144
StatePublished - 2017
Event34th International Conference on Machine Learning, ICML 2017 - Sydney, Australia
Duration: Aug 6 2017Aug 11 2017

Publication series

Name34th International Conference on Machine Learning, ICML 2017
Volume8

Other

Other34th International Conference on Machine Learning, ICML 2017
CountryAustralia
CitySydney
Period8/6/178/11/17

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Human-Computer Interaction
  • Software

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