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Confidence Bands In Quantile Regression

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  • Härdle, Wolfgang K.
  • Song, Song

Abstract

Let ( X 1 , Y 1 ), …, ( X , Y ) 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 l ( 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 { l ( x ) – l ( x )}. Using strong approximations of the empirical process and extreme value theory, we consider the asymptotic maximal deviation sup 0≤ | l ( 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(04), pages 1180-1200, August.
  • Handle: RePEc:cup:etheor:v:26:y:2010:i:04:p:1180-1200_99
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    References listed on IDEAS

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    1. Murphy, Kevin M & Welch, Finis, 1990. "Empirical Age-Earnings Profiles," Journal of Labor Economics, University of Chicago Press, vol. 8(2), pages 202-229, April.
    2. Jeong, Kiho & Härdle, Wolfgang K. & Song, Song, 2012. "A Consistent Nonparametric Test For Causality In Quantile," Econometric Theory, Cambridge University Press, vol. 28(04), pages 861-887, August.
    3. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, March.
    4. Kong, Efang & Linton, Oliver & Xia, Yingcun, 2010. "Uniform Bahadur Representation For Local Polynomial Estimates Of M-Regression And Its Application To The Additive Model," Econometric Theory, Cambridge University Press, vol. 26(05), pages 1529-1564, October.
    5. Haerdle,W. & Janssen,P. & Serfling,R., 1986. "Strong uniform consistency rates for estimators of conditional functionals," Discussion Paper Serie A 63, University of Bonn, Germany.
    6. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    7. Lejeune, Michel G. & Sarda, Pascal, 1988. "Quantile regression: a nonparametric approach," Computational Statistics & Data Analysis, Elsevier, vol. 6(3), pages 229-239, April.
    8. Cai, Zongwu, 2002. "Regression Quantiles For Time Series," Econometric Theory, Cambridge University Press, vol. 18(01), pages 169-192, February.
    9. Härdle, Wolfgang, 1989. "Asymptotic maximal deviation of M-smoothers," Journal of Multivariate Analysis, Elsevier, vol. 29(2), pages 163-179, May.
    10. Koenker, Roger & Park, Beum J., 1996. "An interior point algorithm for nonlinear quantile regression," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 265-283.
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    Citations

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    Cited by:

    1. 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.
    2. Marc Hallin & Zudi Lu & Davy Paindaveine & Miroslav Siman, 2012. "Local Constant and Local Bilinear Multiple-Output Quantile Regression," Working Papers ECARES ECARES 2012-003, ULB -- Universite Libre de Bruxelles.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    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. 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.
    9. 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.
    10. 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.
    11. 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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