A model-free conditional screening approach via sufficient dimension reduction

ABSTRACT

Conditional variable screening arises when researchers have prior information regarding the importance of certain predictors. It is natural to consider feature screening methods conditioning on these known important predictors. Barut, E., Fan, J., and Verhasselt, A. [(2016), ‘Conditional Sure Independence Screening’, Journal of the American Statistical Association, 111, 1266–1277] proposed conditional sure independence screening (CSIS) to address this issue under the context of generalised linear models. While CSIS outperforms the marginal screening method when few of the factors are known to be important and/or significant correlations between some of the factors exist, unfortunately, CSIS is model based and might fail when the models are misspecified. We propose a model-free conditional screening method under the framework of sufficient dimension reduction for ultrahigh dimensional statistical problems. Numerical studies show our method easily beats CSIS for nonlinear models and performs comparable to CSIS for (generalised) linear models. Sure screening consistency property for our method is proved.

Keywords:

• Conditional screening
• trace pursuit
• variable selection
• sufficient dimension reduction

2010 Mathematics Subject Classification:

• 62G05

Acknowledgements

The authors are grateful to the Associate Editor and two anonymous referees for their constructive comments and suggestions. Zhou Yu's research was partially supported by the National Scientific Foundation of China 11971170, and the Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Zhou Yu's research was partially supported by the National Scientific Foundation of China [grant number 11971170].