Journal
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
Volume 115, Issue 531, Pages 1393-1405Publisher
AMER STATISTICAL ASSOC
DOI: 10.1080/01621459.2019.1632078
Keywords
Cumulative divergence; Feature screening; Forward screening; High dimensionality; Sure screening property; Variable selection
Categories
Funding
- National Natural Science Foundation of China (NNSFC) [11731011, 11690014, 11690015, 11801501]
- NSERC [RGPIN-2016-05024]
- NSF [DMS 1820702]
- NIDA, NIH grant [P50 DA039838]
- Ministry of Education Project of Key Research Institute of Humanities and Social Sciences at Universities [16JJD910002]
- National Youth Top-notch Talent Support Program, P. R. China
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Feature screening plays an important role in the analysis of ultrahigh dimensional data. Due to complicated model structure and high noise level, existing screening methods often suffer from model misspecification and the presence of outliers. To address these issues, we introduce a new metric named cumulative divergence (CD), and develop a CD-based forward screening procedure. This forward screening method is model-free and resistant to the presence of outliers in the response. It also incorporates the joint effects among covariates into the screening process. With a data-driven threshold, the new method can automatically determine the number of features that should be retained after screening. These merits make the CD-based screening very appealing in practice. Under certain regularity conditions, we show that the proposed method possesses sure screening property. The performance of our proposal is illustrated through simulations and a real data example. for this article are available online.
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