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Transformed sufficient dimension reduction

Author

Listed:
  • T. Wang
  • X. Guo
  • L. Zhu
  • P. Xu

Abstract

We propose a general framework for dimension reduction in regression to fill the gap between linear and fully nonlinear dimension reduction. The main idea is to first transform each of the raw predictors monotonically and then search for a low-dimensional projection in the space defined by the transformed variables. Both user-specified and data-driven transformations are suggested. In each case, the methodology is first discussed in generality and then a representative method is proposed and evaluated by simulation. The proposed methods are applied to a real dataset.

Suggested Citation

  • T. Wang & X. Guo & L. Zhu & P. Xu, 2014. "Transformed sufficient dimension reduction," Biometrika, Biometrika Trust, vol. 101(4), pages 815-829.
    • Handle: RePEc:oup:biomet:v:101:y:2014:i:4:p:815-829.
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    File URL: http://hdl.handle.net/10.1093/biomet/asu037
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    Cited by:

    1. Tao, Chenyang & Feng, Jianfeng, 2017. "Canonical kernel dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 107(C), pages 131-148.
    2. Dong, Yuexiao & Yang, Chaozheng & Yu, Zhou, 2016. "On permutation tests for predictor contribution in sufficient dimension reduction," Journal of Multivariate Analysis, Elsevier, vol. 149(C), pages 81-91.
    3. Zhou, Jingke & Zhu, Lixing, 2016. "Principal minimax support vector machine for sufficient dimension reduction with contaminated data," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 33-48.

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