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Sufficient dimension reduction using Hilbert–Schmidt independence criterion

Author

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  • Xue, Yuan
  • Zhang, Nan
  • Yin, Xiangrong
  • Zheng, Haitao

Abstract

By using Hilbert–Schmidt Independence Criterion, a sufficient dimension reduction method is proposed to estimate the directions in multiple-index models. A projection pursuit type of sufficient searching algorithm is introduced to reduce the computational complexity, as the original problem involves non-linear optimization over multidimensional Grassmann-manifold. A bootstrap procedure with additional jump point detection algorithm is used for determining the dimensionality. The proposed method demonstrates competitive performance compared with some well-known dimension reduction methods via simulation studies and an application to a real data.

Suggested Citation

  • Xue, Yuan & Zhang, Nan & Yin, Xiangrong & Zheng, Haitao, 2017. "Sufficient dimension reduction using Hilbert–Schmidt independence criterion," Computational Statistics & Data Analysis, Elsevier, vol. 115(C), pages 67-78.
    • Handle: RePEc:eee:csdana:v:115:y:2017:i:c:p:67-78
    DOI: 10.1016/j.csda.2017.05.002
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    References listed on IDEAS

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    4. Yin, Xiangrong & Li, Bing & Cook, R. Dennis, 2008. "Successive direction extraction for estimating the central subspace in a multiple-index regression," Journal of Multivariate Analysis, Elsevier, vol. 99(8), pages 1733-1757, September.
    5. Wang, Hansheng & Xia, Yingcun, 2008. "Sliced Regression for Dimension Reduction," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 811-821, June.
    6. Ye Z. & Weiss R.E., 2003. "Using the Bootstrap to Select One of a New Class of Dimension Reduction Methods," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 968-979, January.
    7. Sheng, Wenhui & Yin, Xiangrong, 2013. "Direction estimation in single-index models via distance covariance," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 148-161.
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