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Huber-type principal expectile component analysis

Author

Listed:
  • Lin, Liang-Ching
  • Chen, Ray-Bing
  • Huang, Mong-Na Lo
  • Guo, Meihui

Abstract

In principal component analysis (PCA), principal components are identified by maximizing the component score variance around the mean. However, a practitioner might be interested in capturing the variation in the tail rather than the center of a distribution to, for example, identify the major pollutants from air pollution data. To address this problem, we introduce a new method called Huber-type principal expectile component (HPEC) analysis that uses an asymmetric Huber norm to provide a kind of robust-tail PCA. The statistical properties of HPECs are derived, and a derivative-free optimization approach called particle swarm optimization (PSO) is used to identify HPECs numerically. As a demonstration, HPEC analysis is applied to real and simulated data with encouraging results.

Suggested Citation

  • Lin, Liang-Ching & Chen, Ray-Bing & Huang, Mong-Na Lo & Guo, Meihui, 2020. "Huber-type principal expectile component analysis," Computational Statistics & Data Analysis, Elsevier, vol. 151(C).
    • Handle: RePEc:eee:csdana:v:151:y:2020:i:c:s0167947320300839
    DOI: 10.1016/j.csda.2020.106992
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    References listed on IDEAS

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    1. Michael E. Tipping & Christopher M. Bishop, 1999. "Probabilistic Principal Component Analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 611-622.
    2. Tran, Ngoc M. & Burdejová, Petra & Ospienko, Maria & Härdle, Wolfgang K., 2019. "Principal component analysis in an asymmetric norm," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 1-21.
    3. Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-847, July.
    4. James W. Taylor, 2008. "Estimating Value at Risk and Expected Shortfall Using Expectiles," Journal of Financial Econometrics, Oxford University Press, vol. 6(2), pages 231-252, Spring.
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