A consistent variable screening procedure with family-wise error control

ABSTRACT

Variable selection in ultra-high-dimensional data analysis is of critical importance in diverse scientific fields. There are many methods proposed for this problem in the past few decades. However, no attention has been paid on the model size produced by screening procedures and the difficulty of determining the screening threshold for practical use, which is key to real applications. Specifically, the pre-defined model size in a screening procedure lacks theoretical support, and users have no idea about the true positives and false positives in the final results. To solve this problem, we developed a new consistent independence screening procedure called HHG-CIS. The screening threshold of HHG-CIS can be set to explicitly control the family-wise error rate, thus it is easy to use in practice. Furthermore, HHG-CIS is model-free, robust to outliers, and outperforms other methods in models with interactions. We showed these advantages of HHG-CIS through extensive simulations and a real data application.

KEYWORDS:

• Ultra-high dimension
• model-free
• consistent screening
• variable selection
• HHG-CIS

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 00-01
• 99-00

Acknowledgments

The authors would like to thank the Editor, the Associate Editor and the reviewer for their constructive and insightful comments and suggestions that greatly improved the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

ORCID

Xiaodan Fan http://orcid.org/0000-0002-2744-9030

Additional information

Funding

This research is partially supported by two grants from the Research Grants Council of the Hong Kong Special Administrative Region, China (Theme-based Research Scheme T12-402/13N and General Research Fund CUHK14203915), The National Natural Science Foundation of China (11901517) and The Fundamental Research Funds for the Central Universities of China (1A3000*172210192).