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Geoadditive expectile regression

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  • Sobotka, Fabian
  • Kneib, Thomas

Abstract

Quantile regression has emerged as one of the standard tools for regression analysis that enables a proper assessment of the complete conditional distribution of responses even in the presence of heteroscedastic errors. Quantile regression estimates are obtained by minimising an asymmetrically weighted sum of absolute deviations from the regression line, a decision theoretic formulation of the estimation problem that avoids a full specification of the error term distribution. Recent advances in mean regression have concentrated on making the regression structure more flexible by including nonlinear effects of continuous covariates, random effects or spatial effects. These extensions often rely on penalised least squares or penalised likelihood estimation with quadratic penalties and may therefore be difficult to combine with the linear programming approaches often considered in quantile regression. As a consequence, geoadditive expectile regression based on minimising an asymmetrically weighted sum of squared residuals is introduced. Different estimation procedures are presented including least asymmetrically weighted squares, boosting and restricted expectile regression. The properties of these procedures are investigated in a simulation study and an analysis on rental fees in Munich is provided where the geoadditive specification allows for an analysis of nonlinear effects of the size of flats or the year of construction and the spatial distribution of rents simultaneously.

Suggested Citation

  • Sobotka, Fabian & Kneib, Thomas, 2012. "Geoadditive expectile regression," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 755-767.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:4:p:755-767
    DOI: 10.1016/j.csda.2010.11.015
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    References listed on IDEAS

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    Cited by:

    1. Taoufik Bouezmarni & Mohamed Doukali & Abderrahim Taamouti, 2023. "Testing Granger Non-Causality in Expectiles," University of East Anglia School of Economics Working Paper Series 2023-02, School of Economics, University of East Anglia, Norwich, UK..
    2. Otto-Sobotka, Fabian & Salvati, Nicola & Ranalli, Maria Giovanna & Kneib, Thomas, 2019. "Adaptive semiparametric M-quantile regression," Econometrics and Statistics, Elsevier, vol. 11(C), pages 116-129.
    3. Marco Alfò & Maria Francesca Marino & Maria Giovanna Ranalli & Nicola Salvati & Nikos Tzavidis, 2021. "M‐quantile regression for multivariate longitudinal data with an application to the Millennium Cohort Study," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(1), pages 122-146, January.
    4. Daouia, Abdelaati & Girard, Stéphane & Stupfler, Gilles, 2018. "Tail expectile process and risk assessment," TSE Working Papers 18-944, Toulouse School of Economics (TSE).
    5. Wang, Bingling & Li, Yingxing & Härdle, Wolfgang Karl, 2022. "K-expectiles clustering," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    6. Abdelaati Daouia & Gilles Stupfler & Antoine Usseglio-Carleve, 2024. "An expectile computation cookbook," Post-Print hal-04524319, HAL.
    7. Ngandu Balekelayi & Solomon Tesfamariam, 2020. "Geoadditive Quantile Regression Model for Sewer Pipes Deterioration Using Boosting Optimization Algorithm," Sustainability, MDPI, vol. 12(20), pages 1-24, October.
    8. Zhao, Jun & Chen, Yingyu & Zhang, Yi, 2018. "Expectile regression for analyzing heteroscedasticity in high dimension," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 304-311.
    9. Taoufik Bouezmarni & Mohamed Doukali & Abderrahim Taamouti, 2022. "Testing Granger Non-Causality in Expectiles," Working Papers 202207, University of Liverpool, Department of Economics.
    10. Garcia-Jorcano, Laura & Sanchis-Marco, Lidia, 2021. "Systemic-systematic risk in financial system: A dynamic ranking based on expectiles," International Review of Economics & Finance, Elsevier, vol. 75(C), pages 330-365.
    11. Alexander Silbersdorff & Kai Sebastian Schneider, 2019. "Distributional Regression Techniques in Socioeconomic Research on the Inequality of Health with an Application on the Relationship between Mental Health and Income," IJERPH, MDPI, vol. 16(20), pages 1-28, October.
    12. Farooq, Muhammad & Steinwart, Ingo, 2017. "An SVM-like approach for expectile regression," Computational Statistics & Data Analysis, Elsevier, vol. 109(C), pages 159-181.
    13. Jun Zhao & Guan’ao Yan & Yi Zhang, 2022. "Robust estimation and shrinkage in ultrahigh dimensional expectile regression with heavy tails and variance heterogeneity," Statistical Papers, Springer, vol. 63(1), pages 1-28, February.
    14. Daouia, Abdelaati & Girard, Stéphane & Stupfler, Gilles, 2021. "ExpectHill estimation, extreme risk and heavy tails," Journal of Econometrics, Elsevier, vol. 221(1), pages 97-117.
    15. Laura Garcia-Jorcano & Lidia Sanchis-Marco, 2023. "Measuring Systemic Risk Using Multivariate Quantile-Located ES Models," Journal of Financial Econometrics, Oxford University Press, vol. 21(1), pages 1-72.
    16. Daouia, Abdelaati & Paindaveine, Davy, 2019. "Multivariate Expectiles, Expectile Depth and Multiple-Output Expectile Regression," TSE Working Papers 19-1022, Toulouse School of Economics (TSE), revised Feb 2023.
    17. V. Maume-Deschamps & D. Rullière & A. Usseglio-Carleve, 2018. "Spatial Expectile Predictions for Elliptical Random Fields," Methodology and Computing in Applied Probability, Springer, vol. 20(2), pages 643-671, June.
    18. Huang, Xiaolin & Shi, Lei & Suykens, Johan A.K., 2014. "Asymmetric least squares support vector machine classifiers," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 395-405.
    19. Daouia, Abdelaati & Stupfler, Gilles & Usseglio-Carleve, Antoine, 2023. "An expectile computation cookbook," TSE Working Papers 23-1458, Toulouse School of Economics (TSE).
    20. Garcia-Jorcano, Laura & Sanchis-Marco, Lidia, 2022. "Spillover effects between commodity and stock markets: A SDSES approach," Resources Policy, Elsevier, vol. 79(C).
    21. Thomschke, Lorenz, 2015. "Changes in the distribution of rental prices in Berlin," Regional Science and Urban Economics, Elsevier, vol. 51(C), pages 88-100.
    22. Kneib, Thomas & Silbersdorff, Alexander & Säfken, Benjamin, 2023. "Rage Against the Mean – A Review of Distributional Regression Approaches," Econometrics and Statistics, Elsevier, vol. 26(C), pages 99-123.
    23. James Dawber & Nicola Salvati & Enrico Fabrizi & Nikos Tzavidis, 2022. "Expectile regression for multi‐category outcomes with application to small area estimation of labour force participation," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(S2), pages 590-619, December.
    24. Songfeng Zheng, 2021. "KLERC: kernel Lagrangian expectile regression calculator," Computational Statistics, Springer, vol. 36(1), pages 283-311, March.

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