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Canonical kernel dimension reduction

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  • Tao, Chenyang
  • Feng, Jianfeng

Abstract

A new kernel dimension reduction (KDR) method based on the gradient space of canonical functions is proposed for sufficient dimension reduction (SDR). Similar to existing KDR methods, this new method achieves SDR for arbitrary distributions, but with more flexibility and improved computational efficiency. The choice of loss function in cross-validation is discussed, and a two-stage screening procedure is proposed. Empirical evidence shows that the new method yields favorable performance, both in terms of accuracy and scalability, especially for large and more challenging datasets compared with other distribution-free SDR methods.

Suggested Citation

  • Tao, Chenyang & Feng, Jianfeng, 2017. "Canonical kernel dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 107(C), pages 131-148.
    • Handle: RePEc:eee:csdana:v:107:y:2017:i:c:p:131-148
    DOI: 10.1016/j.csda.2016.10.003
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    References listed on IDEAS

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    1. Zhu, Yu & Zeng, Peng, 2006. "Fourier Methods for Estimating the Central Subspace and the Central Mean Subspace in Regression," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1638-1651, December.
    2. Yingcun Xia & Howell Tong & W. K. Li & Li‐Xing Zhu, 2002. "An adaptive estimation of dimension reduction space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 363-410, August.
    3. 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.
    4. T. Wang & X. Guo & L. Zhu & P. Xu, 2014. "Transformed sufficient dimension reduction," Biometrika, Biometrika Trust, vol. 101(4), pages 815-829.
    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. Zeng, Peng & Zhu, Yu, 2010. "An integral transform method for estimating the central mean and central subspaces," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 271-290, January.
    7. Xiangrong Yin & R. Dennis Cook, 2005. "Direction estimation in single-index regressions," Biometrika, Biometrika Trust, vol. 92(2), pages 371-384, June.
    8. Jianqing Fan & Jinchi Lv, 2008. "Sure independence screening for ultrahigh dimensional feature space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 849-911, November.
    9. Cook, R. Dennis & Ni, Liqiang, 2005. "Sufficient Dimension Reduction via Inverse Regression: A Minimum Discrepancy Approach," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 410-428, June.
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