IDEAS home Printed from https://ideas.repec.org/a/spr/alstar/v96y2012i4p517-541.html
   My bibliography  Save this article

Simultaneous confidence bands for expectile functions

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10182-011-0182-1
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10182-011-0182-1?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. Härdle, Wolfgang Karl & Ritov, Ya'acov & Song, Song, 2010. "Partial linear quantile regression and bootstrap confidence bands," SFB 649 Discussion Papers 2010-002, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    3. 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.
    4. Diebold, Francis X. & Inoue, Atsushi, 2001. "Long memory and regime switching," Journal of Econometrics, Elsevier, vol. 105(1), pages 131-159, November.
    5. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731.
    6. Yao, Qiwei & Tong, Howell, 1996. "Asymmetric least squares regression estimation: a nonparametric approach," LSE Research Online Documents on Economics 19423, London School of Economics and Political Science, LSE Library.
    7. Johnston, Gordon J., 1982. "Probabilities of maximal deviations for nonparametric regression function estimates," Journal of Multivariate Analysis, Elsevier, vol. 12(3), pages 402-414, September.
    8. Jones, M. C., 1994. "Expectiles and M-quantiles are quantiles," Statistics & Probability Letters, Elsevier, vol. 20(2), pages 149-153, May.
    9. James W. Taylor, 2008. "Estimating Value at Risk and Expected Shortfall Using Expectiles," Journal of Financial Econometrics, Oxford University Press, vol. 6(2), pages 231-252, Spring.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. repec:hum:wpaper:sfb649dp2014-028 is not listed on IDEAS
    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, 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.
    5. repec:hum:wpaper:sfb649dp2014-021 is not listed on IDEAS
    6. 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.
    7. repec:hum:wpaper:sfb649dp2014-059 is not listed on IDEAS
    8. repec:hum:wpaper:sfb649dp2013-001 is not listed on IDEAS
    9. 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.
    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. repec:hum:wpaper:sfb649dp2015-029 is not listed on IDEAS
    12. 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.
    13. 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.
    14. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hamidi, Benjamin & Maillet, Bertrand & Prigent, Jean-Luc, 2014. "A dynamic autoregressive expectile for time-invariant portfolio protection strategies," Journal of Economic Dynamics and Control, Elsevier, vol. 46(C), pages 1-29.
    2. Duran, Esra Akdeniz & Guo, Mengmeng & Härdle, Wolfgang Karl, 2010. "A confidence corridor for expectile functions," SFB 649 Discussion Papers 2011-004, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    3. James Ming Chen, 2018. "On Exactitude in Financial Regulation: Value-at-Risk, Expected Shortfall, and Expectiles," Risks, MDPI, vol. 6(2), pages 1-28, June.
    4. 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.
    5. Xiu Xu & Andrija Mihoci & Wolfgang Karl Hardle, 2020. "lCARE -- localizing Conditional AutoRegressive Expectiles," Papers 2009.13215, arXiv.org.
    6. Xu, Xiu & Mihoci, Andrija & Härdle, Wolfgang Karl, 2018. "lCARE - localizing conditional autoregressive expectiles," Journal of Empirical Finance, Elsevier, vol. 48(C), pages 198-220.
    7. repec:hum:wpaper:sfb649dp2013-001 is not listed on IDEAS
    8. Härdle, Wolfgang Karl & Ling, Chengxiu, 2018. "How Sensitive are Tail-related Risk Measures in a Contamination Neighbourhood?," IRTG 1792 Discussion Papers 2018-010, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    9. Mohammedi, Mustapha & Bouzebda, Salim & Laksaci, Ali, 2021. "The consistency and asymptotic normality of the kernel type expectile regression estimator for functional data," Journal of Multivariate Analysis, Elsevier, vol. 181(C).
    10. repec:hum:wpaper:sfb649dp2015-052 is not listed on IDEAS
    11. Taylor, James W., 2021. "Evaluating quantile-bounded and expectile-bounded interval forecasts," International Journal of Forecasting, Elsevier, vol. 37(2), pages 800-811.
    12. Antonio Rubia Serrano & Lidia Sanchis-Marco, 2015. "Measuring Tail-Risk Cross-Country Exposures in the Banking Industry," Working Papers. Serie AD 2015-01, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    13. Zongwu Cai & Ying Fang & Dingshi Tian, 2018. "Assessing Tail Risk Using Expectile Regressions with Partially Varying Coefficients," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201804, University of Kansas, Department of Economics, revised Oct 2018.
    14. 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.
    15. Taoufik Bouezmarni & Mohamed Doukali & Abderrahim Taamouti, 2024. "Testing Granger non-causality in expectiles," Econometric Reviews, Taylor & Francis Journals, vol. 43(1), pages 30-51, January.
    16. Zhang, Feipeng & Xu, Yixiong & Fan, Caiyun, 2023. "Nonparametric inference of expectile-based value-at-risk for financial time series with application to risk assessment," International Review of Financial Analysis, Elsevier, vol. 90(C).
    17. 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.
    18. Bellini, Fabio & Klar, Bernhard & Müller, Alfred & Rosazza Gianin, Emanuela, 2014. "Generalized quantiles as risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 41-48.
    19. Abdelaati Daouia & Simone A. Padoan & Gilles Stupfler, 2024. "Extreme expectile estimation for short-tailed data," Post-Print hal-04672516, HAL.
    20. Busetti, Fabio & Caivano, Michele & Delle Monache, Davide & Pacella, Claudia, 2021. "The time-varying risk of Italian GDP," Economic Modelling, Elsevier, vol. 101(C).
    21. repec:dau:papers:123456789/15232 is not listed on IDEAS
    22. Bonaccolto, Giovanni & Caporin, Massimiliano & Maillet, Bertrand B., 2022. "Dynamic large financial networks via conditional expected shortfalls," European Journal of Operational Research, Elsevier, vol. 298(1), pages 322-336.
    23. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:alstar:v:96:y:2012:i:4:p:517-541. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.