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Confidence Corridors for Multivariate Generalized Quantile Regression

Author

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  • Shih-Kang Chao
  • Katharina Proksch
  • Holger Dette
  • Wolfgang Karl Härdle

Abstract

We focus on the construction of confidence corridors for multivariate nonparametric generalized quantile regression functions. This construction is based on asymptotic results for the maximal deviation between a suitable nonparametric estimator and the true function of interest, which follow after a series of approximation steps including a Bahadur representation, a new strong approximation theorem, and exponential tail inequalities for Gaussian random fields. As a byproduct we also obtain multivariate confidence corridors for the regression function in the classical mean regression. To deal with the problem of slowly decreasing error in coverage probability of the asymptotic confidence corridors, which results in meager coverage for small sample sizes, a simple bootstrap procedure is designed based on the leading term of the Bahadur representation. The finite-sample properties of both procedures are investigated by means of a simulation study and it is demonstrated that the bootstrap procedure considerably outperforms the asymptotic bands in terms of coverage accuracy. Finally, the bootstrap confidence corridors are used to study the efficacy of the National Supported Work Demonstration, which is a randomized employment enhancement program launched in the 1970s. This article has supplementary materials online.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:jnlbes:v:35:y:2017:i:1:p:70-85
    DOI: 10.1080/07350015.2015.1054493
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    Cited by:

    1. 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".
    2. Chao, Shih-Kang & Härdle, Wolfgang K. & Huang, Chen, 2018. "Multivariate factorizable expectile regression with application to fMRI data," Computational Statistics & Data Analysis, Elsevier, vol. 121(C), pages 1-19.
    3. Dette, Holger & Melas, Viatcheslav B. & Shpilev, Petr, 2017. "T-optimal discriminating designs for Fourier regression models," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 196-206.
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    6. Chao, Shih-Kang & Härdle, Wolfgang Karl & Huang, Chen, 2016. "Multivariate factorisable sparse asymmetric least squares regression," SFB 649 Discussion Papers 2016-058, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    7. Kim, Kun Ho & Chao, Shih-Kang & Härdle, Wolfgang Karl, 2016. "Simultaneous inference for the partially linear model with a multivariate unknown function when the covariates are measured with errors," SFB 649 Discussion Papers 2016-024, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.

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    JEL classification:

    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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