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Sliced inverse median difference regression

Author

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  • Stephen Babos

    (Cardiff University)

  • Andreas Artemiou

    (Cardiff University)

Abstract

In this paper we propose a sufficient dimension reduction algorithm based on the difference of inverse medians. The classic methodology based on inverse means in each slice was recently extended, by using inverse medians, to robustify existing methodology at the presence of outliers. Our effort is focused on using differences between inverse medians in pairs of slices. We demonstrate that our method outperforms existing methods at the presence of outliers. We also propose a second algorithm which is not affected by the ordering of slices when the response variable is categorical with no underlying ordering of its values.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stmapp:v:29:y:2020:i:4:d:10.1007_s10260-020-00509-7
    DOI: 10.1007/s10260-020-00509-7
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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.
    2. 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.
    3. 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.
    4. Artemiou, Andreas & Tian, Lipu, 2015. "Using sliced inverse mean difference for sufficient dimension reduction," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 184-190.
    5. Dong, Yuexiao & Yu, Zhou & Zhu, Liping, 2015. "Robust inverse regression for dimension reduction," Journal of Multivariate Analysis, Elsevier, vol. 134(C), pages 71-81.
    6. 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.
    7. Yongwu Shao & R. Dennis Cook & Sanford Weisberg, 2007. "Marginal tests with sliced average variance estimation," Biometrika, Biometrika Trust, vol. 94(2), pages 285-296.
    8. Wei Luo & Bing Li, 2016. "Combining eigenvalues and variation of eigenvectors for order determination," Biometrika, Biometrika Trust, vol. 103(4), pages 875-887.
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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.

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