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Partial Linear Quantile Regression and Bootstrap Confidence Bands

Author

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  • Wolfgang Karl Härdle
  • Ya’acov Ritov
  • Song Song

Abstract

In this paper uniform confidence bands are constructed for nonparametric quantile estimates of regression functions. The method is based on the bootstrap, where resampling is done from a suitably estimated empirical density function (edf) for residuals. It is known that the approximation error for the uniform confidence band by the asymptotic Gumbel distribution is logarithmically slow. It is proved that the bootstrap approximation provides a substantial improvement. The case of multidimensional and discrete regressor variables is dealt with using a partial linear model. Comparison to classic asymptotic uniform bands is presented through a simulation study. An economic application considers the labour market differential effect with respect to different education levels.

Suggested Citation

  • Wolfgang Karl Härdle & Ya’acov Ritov & Song Song, 2010. "Partial Linear Quantile Regression and Bootstrap Confidence Bands," SFB 649 Discussion Papers SFB649DP2010-002, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    • Handle: RePEc:hum:wpaper:sfb649dp2010-002
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    References listed on IDEAS

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    Cited by:

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    2. Agnieszka Janek & Tino Kluge & Rafal Weron & Uwe Wystup, 2010. "FX Smile in the Heston Model," HSC Research Reports HSC/10/02, Hugo Steinhaus Center, Wroclaw University of Technology.
    3. Nikolaus Hautsch & Peter Malec & Melanie Schienle, 2014. "Capturing the Zero: A New Class of Zero-Augmented Distributions and Multiplicative Error Processes," Journal of Financial Econometrics, Oxford University Press, vol. 12(1), pages 89-121.
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    5. Basteck, Christian & Daniëls, Tijmen R., 2011. "Every symmetric 3×3 global game of strategic complementarities has noise-independent selection," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 749-754.
    6. Franziska Schulze, 2010. "Spatial Dependencies in German Matching Functions," SFB 649 Discussion Papers SFB649DP2010-054, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    7. Alexander L. Baranovski, 2010. "Dynamical systems forced by shot noise as a new paradigm in the interest rate modeling," SFB 649 Discussion Papers SFB649DP2010-037, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    8. Ulrich Horst & Santiago Moreno-Bromberg, 2010. "Efficiency and Equilibria in Games of Optimal Derivative Design," SFB 649 Discussion Papers SFB649DP2010-035, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    9. Szymon Borak & Adam Misiorek & Rafał Weron, 2010. "Models for Heavy-tailed Asset Returns," SFB 649 Discussion Papers SFB649DP2010-049, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    10. Enno Mammen & Christoph Rothe & Melanie Schienle, 2010. "Nonparametric Regression with Nonparametrically Generated Covariates," SFB 649 Discussion Papers SFB649DP2010-059, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    11. Wolfgang Karl Härdle & Ya'acov Ritov & Weining Wang, 2013. "Tie the straps: uniform bootstrap confidence bands for bounded influence curve estimators," SFB 649 Discussion Papers SFB649DP2013-047, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    12. Ralf Sabiwalsky, 2010. "Executive Compensation Regulation and the Dynamics of the Pay-Performance Sensitivity," SFB 649 Discussion Papers SFB649DP2010-051, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    13. Shih-Kang Chao & Wolfgang Karl Härdle & Weining Wang, 2012. "Quantile Regression in Risk Calibration," SFB 649 Discussion Papers SFB649DP2012-006, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    14. Carolin Hecht & Katja Hanewald, 2010. "Sociodemographic, Economic, and Psychological Drivers of the Demand for Life Insurance: Evidence from the German Retirement Income Act," SFB 649 Discussion Papers SFB649DP2010-034, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    15. Vladimir Panov, 2010. "Estimation of the signal subspace without estimation of the inverse covariance matrix," SFB 649 Discussion Papers SFB649DP2010-050, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    16. 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.
    17. Maria Grith & Volker Krätschmer, 2010. "Parametric estimation of risk neutral density functions," SFB 649 Discussion Papers SFB649DP2010-045, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

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    More about this item

    Keywords

    Bootstrap; Quantile Regression; Confidence Bands; Nonparametric Fitting; Kernel Smoothing; Partial Linear Model;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • J01 - Labor and Demographic Economics - - General - - - Labor Economics: General
    • J31 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs - - - Wage Level and Structure; Wage Differentials
    • J71 - Labor and Demographic Economics - - Labor Discrimination - - - Hiring and Firing

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