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Bootstrap confidence bands and partial linear quantile regression

Author

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  • Song, Song
  • Ritov, Ya’acov
  • Härdle, Wolfgang K.

Abstract

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

Suggested Citation

  • 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.
  • Handle: RePEc:eee:jmvana:v:107:y:2012:i:c:p:244-262
    DOI: 10.1016/j.jmva.2012.01.020
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    References listed on IDEAS

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    Cited by:

    1. Fan, Yanqin & Liu, Ruixuan, 2016. "A direct approach to inference in nonparametric and semiparametric quantile models," Journal of Econometrics, Elsevier, vol. 191(1), pages 196-216.
    2. 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.
    3. Qu, Zhongjun & Yoon, Jungmo, 2015. "Nonparametric estimation and inference on conditional quantile processes," Journal of Econometrics, Elsevier, vol. 185(1), pages 1-19.
    4. Wu, Chaojiang & Yu, Yan, 2014. "Partially linear modeling of conditional quantiles using penalized splines," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 170-187.

    More about this item

    Keywords

    Bootstrap; Quantile regression; Confidence bands; Nonparametric fitting; Kernel smoothing; Partial linear model;

    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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