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Principal component analysis in an asymmetric norm

Author

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  • Tran, Ngoc Mai
  • Burdejová, Petra
  • Osipenko, Maria
  • Härdle, Wolfgang Karl

Abstract

Principal component analysis (PCA) is a widely used dimension reduction tool in the analysis of high-dimensional data. However, in many applications such as risk quantification in finance or climatology, one is interested in capturing the tail variations rather than variation around the mean. In this paper, we develop Principal Expectile Analysis (PEC), which generalizes PCA for expectiles. It can be seen as a dimension reduction tool for extreme value theory, where one approximates uctuations in the expectile level of the data by a low dimensional subspace. We provide algorithms based on iterative least squares, prove upper bounds on their convergence times, and compare their performances in a simulation study. We apply the algorithms to a Chinese weather dataset and fMRI data from an investment decision study.

Suggested Citation

  • Tran, Ngoc Mai & Burdejová, Petra & Osipenko, Maria & Härdle, Wolfgang Karl, 2016. "Principal component analysis in an asymmetric norm," SFB 649 Discussion Papers 2016-040, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    • Handle: RePEc:zbw:sfb649:sfb649dp2016-040
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    References listed on IDEAS

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    Cited by:

    1. Ana C S Costa & Diego E Pereira & Caio M Veríssimo & Marcos A D Bomfim & Rita C R E Queiroga & Marta S Madruga & Susana Alves & Rui J B Bessa & Maria E G Oliveira & Juliana K B Soares, 2019. "Developing cookies formulated with goat cream enriched with conjugated linoleic acid," PLOS ONE, Public Library of Science, vol. 14(9), pages 1-15, September.
    2. 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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    4. Wang, Bingling & Li, Yingxing & Härdle, Wolfgang Karl, 2022. "K-expectiles clustering," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
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    6. 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).

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    JEL classification:

    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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