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Using sliced inverse mean difference for sufficient dimension reduction

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  • Artemiou, Andreas
  • Tian, Lipu

Abstract

We present two different algorithms for sufficient dimension reduction based on the difference between inverse means. We discuss the theoretical properties and demonstrate the computational advantages over SIR (Li, 1991) and CUME (Zhu et al., 2010).

Suggested Citation

  • Artemiou, Andreas & Tian, Lipu, 2015. "Using sliced inverse mean difference for sufficient dimension reduction," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 184-190.
    • Handle: RePEc:eee:stapro:v:106:y:2015:i:c:p:184-190
    DOI: 10.1016/j.spl.2015.07.025
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    References listed on IDEAS

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    1. 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.
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    3. Bura, E. & Yang, J., 2011. "Dimension estimation in sufficient dimension reduction: A unifying approach," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 130-142, January.
    4. Zhu, Li-Ping & Zhu, Li-Xing & Feng, Zheng-Hui, 2010. "Dimension Reduction in Regressions Through Cumulative Slicing Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1455-1466.
    5. Li, Bing & Wang, Shaoli, 2007. "On Directional Regression for Dimension Reduction," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 997-1008, September.
    6. Yongwu Shao & R. Dennis Cook & Sanford Weisberg, 2007. "Marginal tests with sliced average variance estimation," Biometrika, Biometrika Trust, vol. 94(2), pages 285-296.
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    Cited by:

    1. Stephen Babos & Andreas Artemiou, 2021. "Cumulative Median Estimation for Sufficient Dimension Reduction," Stats, MDPI, vol. 4(1), pages 1-8, February.
    2. Stephen Babos & Andreas Artemiou, 2020. "Sliced inverse median difference regression," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(4), pages 937-954, December.

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