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Robust PCA for skewed data and its outlier map

Author

Listed:
  • Hubert, Mia
  • Rousseeuw, Peter
  • Verdonck, Tim

Abstract

The outlier sensitivity of classical principal component analysis (PCA) has spurred the development of robust techniques. Existing robust PCA methods like ROBPCA work best if the non-outlying data have an approximately symmetric distribution. When the original variables are skewed, too many points tend to be flagged as outlying. A robust PCA method is developed which is also suitable for skewed data. To flag the outliers a new outlier map is defined. Its performance is illustrated on real data from economics, engineering, and finance, and confirmed by a simulation study.

Suggested Citation

  • Hubert, Mia & Rousseeuw, Peter & Verdonck, Tim, 2009. "Robust PCA for skewed data and its outlier map," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2264-2274, April.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:6:p:2264-2274
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    References listed on IDEAS

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    1. Croux, Christophe & Ruiz-Gazen, Anne, 2005. "High breakdown estimators for principal components: the projection-pursuit approach revisited," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 206-226, July.
    2. Hubert, Mia & Engelen, Sanne, 2007. "Fast cross-validation of high-breakdown resampling methods for PCA," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 5013-5024, June.
    3. Serneels, Sven & Verdonck, Tim, 2008. "Principal component analysis for data containing outliers and missing elements," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1712-1727, January.
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    3. Boente, Graciela & Pires, Ana M. & Rodrigues, Isabel M., 2010. "Detecting influential observations in principal components and common principal components," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 2967-2975, December.
    4. Debruyne, Michiel & Hubert, Mia & Van Horebeek, Johan, 2010. "Detecting influential observations in Kernel PCA," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3007-3019, December.
    5. Szafranek, Karol, 2021. "Evidence on time-varying inflation synchronization," Economic Modelling, Elsevier, vol. 94(C), pages 1-13.
    6. Václav Plevka & Pieter Segaert & Chris M. J. Tampère & Mia Hubert, 2016. "Analysis of travel activity determinants using robust statistics," Transportation, Springer, vol. 43(6), pages 979-996, November.
    7. Marianna Succurro, 2017. "Financial Bankruptcy across European Countries," International Journal of Economics and Finance, Canadian Center of Science and Education, vol. 9(7), pages 132-146, July.
    8. Huang, Xiaolin & Shi, Lei & Pelckmans, Kristiaan & Suykens, Johan A.K., 2014. "Asymmetric ν-tube support vector regression," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 371-382.
    9. Stephane Heritier & Maria-Pia Victoria-Feser, 2018. "Discussion of “The power of monitoring: how to make the most of a contaminated multivariate sample” by Andrea Cerioli, Marco Riani, Anthony C. Atkinson and Aldo Corbellini," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(4), pages 595-602, December.
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    11. Iaci, Ross & Sriram, T.N., 2013. "Robust multivariate association and dimension reduction using density divergences," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 281-295.
    12. Osipenko, Maria, 2021. "Directional assessment of traffic flow extremes," Transportation Research Part B: Methodological, Elsevier, vol. 150(C), pages 353-369.

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