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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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    1. Gao, Yafeng & Xu, Jiangmin & Yang, Shichao & Tang, Xiaomin & Zhou, Quan & Ge, Jing & Xu, Tengfang & Levinson, Ronnen, 2014. "Cool roofs in China: Policy review, building simulations, and proof-of-concept experiments," Energy Policy, Elsevier, vol. 74(C), pages 190-214.
    2. Kuan, Chung-Ming & Yeh, Jin-Huei & Hsu, Yu-Chin, 2009. "Assessing value at risk with CARE, the Conditional Autoregressive Expectile models," Journal of Econometrics, Elsevier, vol. 150(2), pages 261-270, June.
    3. 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.
    4. Burdejova, P. & Härdle, W. & Kokoszka, P. & Xiong, Q., 2017. "Change point and trend analyses of annual expectile curves of tropical storms," Econometrics and Statistics, Elsevier, vol. 1(C), pages 101-117.
    5. Majer, Piotr & Mohr, Peter N. C. & Heekeren, Hauke R. & Härdle, Wolfgang Karl, 2014. "Portfolio decisions and brain reactions via the CEAD method," SFB 649 Discussion Papers 2014-036, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    6. Fraiman, Ricardo & Pateiro-López, Beatriz, 2012. "Quantiles for finite and infinite dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 108(C), pages 1-14.
    7. Abdelaati Daouia & Stéphane Girard & Gilles Stupfler, 2018. "Estimation of tail risk based on extreme expectiles," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(2), pages 263-292, March.
    8. Zhang, Lingsong & Lu, Shu & Marron, J.S., 2015. "Nested nonnegative cone analysis," Computational Statistics & Data Analysis, Elsevier, vol. 88(C), pages 100-110.
    9. Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-847, July.
    10. Philippe Jorion, 2000. "Risk management lessons from Long‐Term Capital Management," European Financial Management, European Financial Management Association, vol. 6(3), pages 277-300, September.
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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.
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    3. 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.
    4. 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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    6. Wang, Bingling & Li, Yingxing & Härdle, Wolfgang Karl, 2022. "K-expectiles clustering," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    7. Chen, Cathy Yi-Hsuan & Härdle, Wolfgang Karl & Okhrin, Yarema, 2017. "Tail event driven networks of SIFIs," SFB 649 Discussion Papers 2017-004, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    8. repec:hum:wpaper:sfb649dp2016-058 is not listed on IDEAS
    9. 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).
    10. Chao, Shih-Kang & Härdle, Wolfgang Karl & Huang, Chen, 2016. "Multivariate factorisable sparse asymmetric least squares regression," SFB 649 Discussion Papers 2016-058, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    11. 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.

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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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