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Multivariate factorizable expectile regression with application to fMRI data

Author

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  • Chao, Shih-Kang
  • Härdle, Wolfgang K.
  • Huang, Chen

Abstract

A multivariate expectile regression model is proposed to analyze the tail events of large cross-sectional and spatial data, where the tail events are linked by a latent factor structure. The computational advantage of the method is demonstrated, and the estimation risk is analyzed for every fixed number of iteration and fixed sample size, when the latent factors are either exactly or approximately sparse. The proposed method is applied on the functional magnetic resonance imaging (fMRI) data taken during an experiment of investment decisions making. It is shown that the negative extreme blood oxygenation level dependent (BOLD) responses may be relevant to the risk preferences.

Suggested Citation

  • Chao, Shih-Kang & Härdle, Wolfgang K. & Huang, Chen, 2018. "Multivariate factorizable expectile regression with application to fMRI data," Computational Statistics & Data Analysis, Elsevier, vol. 121(C), pages 1-19.
    • Handle: RePEc:eee:csdana:v:121:y:2018:i:c:p:1-19
    DOI: 10.1016/j.csda.2017.12.001
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    References listed on IDEAS

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    1. Chao, Shih-Kang & Härdle, Wolfgang K. & Yuan, Ming, 2021. "Factorisable Multitask Quantile Regression," Econometric Theory, Cambridge University Press, vol. 37(4), pages 794-816, August.
    2. Shih-Kang Chao & Katharina Proksch & Holger Dette & Wolfgang Karl Härdle, 2017. "Confidence Corridors for Multivariate Generalized Quantile Regression," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(1), pages 70-85, January.
    3. Ming Yuan & Ali Ekici & Zhaosong Lu & Renato Monteiro, 2007. "Dimension reduction and coefficient estimation in multivariate linear regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(3), pages 329-346, June.
    4. Izenman, Alan Julian, 1975. "Reduced-rank regression for the multivariate linear model," Journal of Multivariate Analysis, Elsevier, vol. 5(2), pages 248-264, June.
    5. De Rossi, Giuliano & Harvey, Andrew, 2009. "Quantiles, expectiles and splines," Journal of Econometrics, Elsevier, vol. 152(2), pages 179-185, October.
    6. 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.
    7. Colin F. Camerer, 2007. "Neuroeconomics: Using Neuroscience to Make Economic Predictions," Economic Journal, Royal Economic Society, vol. 117(519), pages 26-42, March.
    8. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    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. Alena Bömmel & Song Song & Piotr Majer & Peter Mohr & Hauke Heekeren & Wolfgang Härdle, 2014. "Risk Patterns and Correlated Brain Activities. Multidimensional Statistical Analysis of fMRI Data in Economic Decision Making Study," Psychometrika, Springer;The Psychometric Society, vol. 79(3), pages 489-514, July.
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    Cited by:

    1. Chao, Shih-Kang & Härdle, Wolfgang K. & Yuan, Ming, 2021. "Factorisable Multitask Quantile Regression," Econometric Theory, Cambridge University Press, vol. 37(4), pages 794-816, August.
    2. Hu, Junjie & López Cabrera, Brenda & Melzer, Awdesch, 2021. "Advanced statistical learning on short term load process forecasting," IRTG 1792 Discussion Papers 2021-020, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    3. Christis Katsouris, 2023. "Statistical Estimation for Covariance Structures with Tail Estimates using Nodewise Quantile Predictive Regression Models," Papers 2305.11282, arXiv.org, revised Jul 2023.

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