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Sequential sufficient dimension reduction for large p, small n problems

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  • Xiangrong Yin
  • Haileab Hilafu

Abstract

type="main" xml:id="rssb12093-abs-0001"> We propose a new and simple framework for dimension reduction in the large p, small n setting. The framework decomposes the data into pieces, thereby enabling existing approaches for n>p to be adapted to n>p problems. Estimating a large covariance matrix, which is a very difficult task, is avoided. We propose two separate paths to implement the framework. Our paths provide sufficient procedures for identifying informative variables via a sequential approach. We illustrate the paths by using sufficient dimension reduction approaches, but the paths are very general. Empirical evidence demonstrates the efficacy of our paths. Additional simulations and applications are given in an on-line supplementary file.

Suggested Citation

  • Xiangrong Yin & Haileab Hilafu, 2015. "Sequential sufficient dimension reduction for large p, small n problems," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(4), pages 879-892, September.
    • Handle: RePEc:bla:jorssb:v:77:y:2015:i:4:p:879-892
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    File URL: http://hdl.handle.net/10.1111/rssb.2015.77.issue-4
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    Citations

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    Cited by:

    1. Yang, Baoying & Yin, Xiangrong & Zhang, Nan, 2019. "Sufficient variable selection using independence measures for continuous response," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 480-493.
    2. Wu, Runxiong & Chen, Xin, 2021. "MM algorithms for distance covariance based sufficient dimension reduction and sufficient variable selection," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
    3. Ke, Chenlu & Yang, Wei & Yuan, Qingcong & Li, Lu, 2023. "Partial sufficient variable screening with categorical controls," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).
    4. Xiao, Zhen & Zhang, Qi, 2022. "Dimension reduction for block-missing data based on sparse sliced inverse regression," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).
    5. Hojin Yang & Hongtu Zhu & Joseph G. Ibrahim, 2018. "MILFM: Multiple index latent factor model based on high‐dimensional features," Biometrics, The International Biometric Society, vol. 74(3), pages 834-844, September.
    6. Fang, Fang & Yu, Zhou, 2020. "Model averaging assisted sufficient dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    7. Qin Wang & Yuan Xue, 2023. "A structured covariance ensemble for sufficient dimension reduction," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 17(3), pages 777-800, September.
    8. Emmanuel Jordy Menvouta & Sven Serneels & Tim Verdonck, 2022. "Sparse dimension reduction based on energy and ball statistics," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(4), pages 951-975, December.
    9. Chen, Li-Pang, 2021. "Ultrahigh-dimensional sufficient dimension reduction with measurement error in covariates," Statistics & Probability Letters, Elsevier, vol. 168(C).
    10. Weng, Jiaying, 2022. "Fourier transform sparse inverse regression estimators for sufficient variable selection," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    11. Hung Hung & Su‐Yun Huang, 2019. "Sufficient dimension reduction via random‐partitions for the large‐p‐small‐n problem," Biometrics, The International Biometric Society, vol. 75(1), pages 245-255, March.
    12. Wang, Pei & Yin, Xiangrong & Yuan, Qingcong & Kryscio, Richard, 2021. "Feature filter for estimating central mean subspace and its sparse solution," Computational Statistics & Data Analysis, Elsevier, vol. 163(C).
    13. Yuan, Qingcong & Chen, Xianyan & Ke, Chenlu & Yin, Xiangrong, 2022. "Independence index sufficient variable screening for categorical responses," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).
    14. Wang, Qin & Xue, Yuan, 2021. "An ensemble of inverse moment estimators for sufficient dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 161(C).

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