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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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    References listed on IDEAS

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    Citations

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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. 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.
    3. repec:eee:econom:v:208:y:2019:i:1:p:282-298 is not listed on IDEAS
    4. Brenda López Cabrera & Franziska Schulz, 2017. "Forecasting Generalized Quantiles of Electricity Demand: A Functional Data Approach," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 127-136, January.
    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.

    More about this item

    Keywords

    Asymmetric norm; Dimension reduction; Expectile; Growth data; Quantile; Risk attitude; Temperature;

    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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