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Model-Free Forward Screening Via Cumulative Divergence

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  • Tingyou Zhou
  • Liping Zhu
  • Chen Xu
  • Runze Li

Abstract

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. Supplementary materials for this article are available online.

Suggested Citation

  • Tingyou Zhou & Liping Zhu & Chen Xu & Runze Li, 2020. "Model-Free Forward Screening Via Cumulative Divergence," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(531), pages 1393-1405, July.
    • Handle: RePEc:taf:jnlasa:v:115:y:2020:i:531:p:1393-1405
    DOI: 10.1080/01621459.2019.1632078
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    Cited by:

    1. Xiaochao Xia & Hao Ming, 2022. "A Flexibly Conditional Screening Approach via a Nonparametric Quantile Partial Correlation," Mathematics, MDPI, vol. 10(24), pages 1-32, December.
    2. Xu, Kai & Zhou, Yeqing, 2021. "Projection-averaging-based cumulative covariance and its use in goodness-of-fit testing for single-index models," Computational Statistics & Data Analysis, Elsevier, vol. 164(C).
    3. Joaquim Fernando Pinto da Costa & Manuel Cabral, 2022. "Statistical Methods with Applications in Data Mining: A Review of the Most Recent Works," Mathematics, MDPI, vol. 10(6), pages 1-22, March.
    4. Haofeng Wang & Hongxia Jin & Xuejun Jiang & Jingzhi Li, 2022. "Model Selection for High Dimensional Nonparametric Additive Models via Ridge Estimation," Mathematics, MDPI, vol. 10(23), pages 1-22, December.
    5. Shi, Zhentao & Huang, Jingyi, 2023. "Forward-selected panel data approach for program evaluation," Journal of Econometrics, Elsevier, vol. 234(2), pages 512-535.

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