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Sufficient dimension reduction based on distance‐weighted discrimination

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  • Hayley Randall
  • Andreas Artemiou
  • Xingye Qiao

Abstract

In this paper, we introduce a sufficient dimension reduction (SDR) algorithm based on distance‐weighted discrimination (DWD). Our methods is shown to be robust on the dimension p of the predictors in our problem, and it also utilizes some new computational results in the DWD literature to propose a computationally faster algorithm than previous classification‐based algorithms in the SDR literature. In addition to the theoretical results of similar methods we prove the consistency of our estimate for fixed p. Finally, we demonstrate the advantages of our algorithm using simulated and real datasets.

Suggested Citation

  • Hayley Randall & Andreas Artemiou & Xingye Qiao, 2021. "Sufficient dimension reduction based on distance‐weighted discrimination," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(4), pages 1186-1211, December.
    • Handle: RePEc:bla:scjsta:v:48:y:2021:i:4:p:1186-1211
    DOI: 10.1111/sjos.12484
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    References listed on IDEAS

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    2. Marron, J.S. & Todd, Michael J. & Ahn, Jeongyoun, 2007. "Distance-Weighted Discrimination," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1267-1271, December.
    3. Boxiang Wang & Hui Zou, 2018. "Another look at distance‐weighted discrimination," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(1), pages 177-198, January.
    4. Luke Smallman & Andreas Artemiou, 2017. "A study on imbalance support vector machine algorithms for sufficient dimension reduction," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(6), pages 2751-2763, March.
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    7. Seung Jun Shin & Yichao Wu & Hao Helen Zhang & Yufeng Liu, 2017. "Principal weighted support vector machines for sufficient dimension reduction in binary classification," Biometrika, Biometrika Trust, vol. 104(1), pages 67-81.
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    10. Qiao, Xingye & Zhang, Hao Helen & Liu, Yufeng & Todd, Michael J. & Marron, J. S., 2010. "Weighted Distance Weighted Discrimination and Its Asymptotic Properties," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 401-414.
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