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Student Sliced Inverse Regression

Author

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  • Chiancone, Alessandro
  • Forbes, Florence
  • Girard, Stéphane

Abstract

Sliced Inverse Regression (SIR) has been extensively used to reduce the dimension of the predictor space before performing regression. SIR is originally a model free method but it has been shown to actually correspond to the maximum likelihood of an inverse regression model with Gaussian errors. This intrinsic Gaussianity of standard SIR may explain its high sensitivity to outliers as observed in a number of studies. To improve robustness, the inverse regression formulation of SIR is therefore extended to non-Gaussian errors with heavy-tailed distributions. Considering Student distributed errors it is shown that the inverse regression remains tractable via an Expectation–Maximization (EM) algorithm. The algorithm is outlined and tested in the presence of outliers, both in simulated and real data, showing improved results in comparison to a number of other existing approaches.

Suggested Citation

  • Chiancone, Alessandro & Forbes, Florence & Girard, Stéphane, 2017. "Student Sliced Inverse Regression," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 441-456.
    • Handle: RePEc:eee:csdana:v:113:y:2017:i:c:p:441-456
    DOI: 10.1016/j.csda.2016.08.004
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    References listed on IDEAS

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    8. Marie Chavent & Stéphane Girard & Vanessa Kuentz-Simonet & Benoit Liquet & Thi Nguyen & Jérôme Saracco, 2014. "A sliced inverse regression approach for data stream," Computational Statistics, Springer, vol. 29(5), pages 1129-1152, October.
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    Cited by:

    1. Bousebata, Meryem & Enjolras, Geoffroy & Girard, Stéphane, 2023. "Extreme partial least-squares," Journal of Multivariate Analysis, Elsevier, vol. 194(C).
    2. Girard, Stéphane & Lorenzo, Hadrien & Saracco, Jérôme, 2022. "Advanced topics in Sliced Inverse Regression," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    3. Huiwen Wang & Zhichao Wang & Shanshan Wang, 2021. "Sliced inverse regression method for multivariate compositional data modeling," Statistical Papers, Springer, vol. 62(1), pages 361-393, February.

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