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Confidence Bands In Quantile Regression

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  • Härdle, Wolfgang K.
  • Song, Song

Abstract

Let (X1, Y1), …, (Xn, Yn) be independent and identically distributed random variables and let l(x) be the unknown p-quantile regression curve of Y conditional on X. A quantile smoother ln(x) is a localized, nonlinear estimator of l(x). The strong uniform consistency rate is established under general conditions. In many applications it is necessary to know the stochastic fluctuation of the process {ln(x) – l(x)}. Using strong approximations of the empirical process and extreme value theory, we consider the asymptotic maximal deviation sup0≤x≤1 |ln(x) − l(x)|. The derived result helps in the construction of a uniform confidence band for the quantile curve l(x). This confidence band can be applied as a econometric model check. An economic application considers the relation between age and earnings in the labor market by means of parametric model specification tests, which presents a new framework to describe trends in the entire wage distribution in a parsimonious way.

Suggested Citation

  • Härdle, Wolfgang K. & Song, Song, 2010. "Confidence Bands In Quantile Regression," Econometric Theory, Cambridge University Press, vol. 26(4), pages 1180-1200, August.
    • Handle: RePEc:cup:etheor:v:26:y:2010:i:04:p:1180-1200_99
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    Cited by:

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    2. Song, Song & Ritov, Ya’acov & Härdle, Wolfgang K., 2012. "Bootstrap confidence bands and partial linear quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 244-262.
    3. Härdle, Wolfgang Karl & Ritov, Ya’acov & Wang, Weining, 2015. "Tie the straps: Uniform bootstrap confidence bands for semiparametric additive models," Journal of Multivariate Analysis, Elsevier, vol. 134(C), pages 129-145.
    4. Toshio Honda, 2013. "Nonparametric quantile regression with heavy-tailed and strongly dependent errors," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(1), pages 23-47, February.
    5. Alona Zharova & Andrija Mihoci & Wolfgang Karl Härdle, 2016. "Academic Ranking Scales in Economics: Prediction and Imputation," SFB 649 Discussion Papers SFB649DP2016-020, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    6. 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".
    7. Qu, Zhongjun & Yoon, Jungmo, 2015. "Nonparametric estimation and inference on conditional quantile processes," Journal of Econometrics, Elsevier, vol. 185(1), pages 1-19.
    8. Hasan, Iftekhar & Tunaru, Radu & Vioto, Davide, 2023. "Herding behavior and systemic risk in global stock markets," Journal of Empirical Finance, Elsevier, vol. 73(C), pages 107-133.
    9. Katharina Proksch, 2016. "On confidence bands for multivariate nonparametric regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 68(1), pages 209-236, February.
    10. Duygun, Meryem & Tunaru, Radu & Vioto, Davide, 2021. "Herding by corporates in the US and the Eurozone through different market conditions," Journal of International Money and Finance, Elsevier, vol. 110(C).
    11. 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.
    12. Ali Al-Sharadqah & Majid Mojirsheibani, 2020. "A simple approach to construct confidence bands for a regression function with incomplete data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(1), pages 81-99, March.
    13. Weining Wang & Ihtiyor Bobojonov & Wolfgang Karl Härdle & Martin Odening, 2011. "Increasing Weather Risk: Fact or Fiction?," SFB 649 Discussion Papers SFB649DP2011-077, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    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.

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