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Principal component analysis in an asymmetric norm

Author

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  • Tran, Ngoc M.
  • Burdejová, Petra
  • Ospienko, Maria
  • Härdle, Wolfgang K.

Abstract

Principal component analysis (PCA) is a widely used dimension reduction tool in high-dimensional data analysis. In risk quantification in finance, climatology and many other applications, however, the interest lies in capturing the tail variations rather than variation around the mean. To this end, 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 fluctuations in the τ-expectile level of the data are approximated by a low-dimensional subspace. We provide algorithms based on iterative least squares, derive bounds on their convergence time, and compare their performance through simulations. We apply the algorithms to a Chinese weather dataset and fMRI data from an investment decision study.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:171:y:2019:i:c:p:1-21
    DOI: 10.1016/j.jmva.2018.10.004
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    Cited by:

    1. Petra Burdejová & Wolfgang K. Härdle, 2019. "Dynamic semi-parametric factor model for functional expectiles," Computational Statistics, Springer, vol. 34(2), pages 489-502, June.
    2. Wang, Bingling & Li, Yingxing & Härdle, Wolfgang Karl, 2022. "K-expectiles clustering," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    3. Shih-Kang Chao & Wolfgang K. Härdle & Chen Huang, 2016. "Multivariate Factorisable Sparse Asymmetric Least Squares Regression," SFB 649 Discussion Papers SFB649DP2016-058, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    4. 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).
    5. Chen, Cathy Yi-Hsuan & Härdle, Wolfgang Karl & Okhrin, Yarema, 2019. "Tail event driven networks of SIFIs," Journal of Econometrics, Elsevier, vol. 208(1), pages 282-298.
    6. Cathy Yi-Hsuan Chen & Wolfgang Karl Härdle & Yarema Okhrin, 2017. "Tail event driven networks of SIFIs," SFB 649 Discussion Papers SFB649DP2017-004, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    7. 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.
    8. 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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    More about this item

    Keywords

    Asymmetric norm; Dimension reduction; Expectile; Growth data; Quantile; Risk attitude; Temperature;
    All these keywords.

    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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