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Principal Component Analysis in an Asymmetric Norm

Listed author(s):
  • Ngoc M. Tran
  • Petra Burdejová
  • Maria Osipenko
  • Wolfgang K. Härdle

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 quanti cation in nance 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.

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File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2016-040.pdf
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Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2016-040.

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Length: 38 pages
Date of creation: Oct 2016
Handle: RePEc:hum:wpaper:sfb649dp2016-040
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  1. 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.
  2. Piotr Majer & Peter N. C. Mohr & Hauke R. Heekeren & Wolfgang K. Härdle, 2016. "Portfolio Decisions and Brain Reactions via the CEAD method," Psychometrika, Springer;The Psychometric Society, vol. 81(3), pages 881-903, September.
  3. Kehui Chen & Hans‐Georg Müller, 2012. "Conditional quantile analysis when covariates are functions, with application to growth data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(1), pages 67-89, January.
  4. Sean D. Campbell & Francis X. Diebold, 2005. "Weather Forecasting for Weather Derivatives," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 6-16, March.
  5. Daouia, Abdelaati & Girard, Stéphane & Stupfler, Gilles, 2015. "Estimation of Tail Risk based on Extreme Expectiles," TSE Working Papers 15-566, Toulouse School of Economics (TSE), revised Jul 2017.
  6. Peter Alaton & Boualem Djehiche & David Stillberger, 2002. "On modelling and pricing weather derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 9(1), pages 1-20.
  7. Brenda Lopez Cabrera & Franziska Schulz, 2014. "Forecasting Generalized Quantiles of Electricity Demand: A Functional Data Approach," SFB 649 Discussion Papers SFB649DP2014-030, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  8. Kneip A. & Utikal K. J, 2001. "Inference for Density Families Using Functional Principal Component Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 519-542, June.
  9. Šaltytė Benth, Jūratė & Benth, Fred Espen, 2012. "A critical view on temperature modelling for application in weather derivatives markets," Energy Economics, Elsevier, vol. 34(2), pages 592-602.
  10. James W. Taylor, 2008. "Estimating Value at Risk and Expected Shortfall Using Expectiles," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 6(2), pages 231-252, Spring.
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