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Simultaneous confidence bands for expectile functions

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  • Mengmeng Guo
  • Wolfgang Härdle

Abstract

Expectile regression, as a general M smoother, is used to capture the tail behaviour of a distribution. Let (X 1 ,Y 1 ),…,(X n ,Y n ) be i.i.d. rvs. Denote by v(x) the unknown τ-expectile regression curve of Y conditional on X, and by v n (x) its kernel smoothing estimator. In this paper, we prove the strong uniform consistency rate of v n (x) under general conditions. Moreover, using strong approximations of the empirical process and extreme value theory, we consider the asymptotic maximal deviation sup 0≤x≤1 |v n (x)−v(x)|. According to the asymptotic theory, we construct simultaneous confidence bands around the estimated expectile function. Furthermore, we apply this confidence band to temperature analysis. Taking Berlin and Taipei as an example, we investigate the temperature risk drivers to these two cities. Copyright Springer-Verlag 2012

Suggested Citation

  • Mengmeng Guo & Wolfgang Härdle, 2012. "Simultaneous confidence bands for expectile functions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 96(4), pages 517-541, October.
    • Handle: RePEc:spr:alstar:v:96:y:2012:i:4:p:517-541
    DOI: 10.1007/s10182-011-0182-1
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    References listed on IDEAS

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    Cited by:

    1. Stephan Stahlschmidt & Matthias Eckardt & Wolfgang K. Härdle, 2014. "Expectile Treatment Effects: An efficient alternative to compute the distribution of treatment effects," SFB 649 Discussion Papers SFB649DP2014-059, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    2. Kim, Kun Ho & Chao, Shih-Kang & Härdle, Wolfgang Karl, 2020. "Simultaneous Inference of the Partially Linear Model with a Multivariate Unknown Function," IRTG 1792 Discussion Papers 2020-008, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    3. Stahlschmidt, Stephan & Eckardt, Matthias & Härdle, Wolfgang Karl, 2014. "Expectile treatment effects: An efficient alternative to compute the distribution of treatment effects," SFB 649 Discussion Papers 2014-059, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    4. Xianhua Dai & Wolfgang Karl Härdle & Keming Yu, 2014. "Do Maternal Health Problems Influence Child's Worrying Status? Evidence from British Cohort Study," SFB 649 Discussion Papers SFB649DP2014-021, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    5. 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.
    6. Burdejova, Petra & Härdle, Wolfgang Karl & Kokoszka, Piotr & Xiong, Q., 2015. "Change point and trend analyses of annual expectile curves of tropical storms," SFB 649 Discussion Papers 2015-029, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    7. Dai, Xianhua & Härdle, Wolfgang Karl & Yu, Keming, 2014. "Do maternal health problems influence child's worrying status? Evidence from British cohort study," SFB 649 Discussion Papers 2014-021, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    8. Chao, Shih-kang & Proksch, Katharina & Dette, Holger & Härdle, Wolfgang Karl, 2014. "Confidence corridors for multivariate generalized quantile regression," SFB 649 Discussion Papers 2014-028, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    9. 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.
    10. 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.
    11. Guo, Mengmeng & Zhou, Lhan & Huang, Jianhua Z. & Härdle, Wolfgang Karl, 2013. "Functional data analysis of generalized quantile regressions," SFB 649 Discussion Papers 2013-001, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    12. Stéphane Girard & Gilles Stupfler & Antoine Usseglio‐Carleve, 2022. "Nonparametric extreme conditional expectile estimation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(1), pages 78-115, March.
    13. Xianhua Dai & Wolfgang Karl Härdle & Keming Yu, 2016. "Do maternal health problems influence child's worrying status? Evidence from the British Cohort Study," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(16), pages 2941-2955, December.
    14. Mengmeng Guo & Lhan Zhou & Jianhua Z. Huang & Wolfgang Karl Härdle, 2013. "Functional Data Analysis of Generalized Quantile Regressions," SFB 649 Discussion Papers SFB649DP2013-001, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    15. Mustapha Rachdi & Ali Laksaci & Noriah M. Al-Kandari, 2022. "Expectile regression for spatial functional data analysis (sFDA)," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(5), pages 627-655, July.

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