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Simultaneous confidence interval for quantile regression

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  • Yaeji Lim
  • Hee-Seok Oh

Abstract

This paper considers a problem of constructing simultaneous confidence intervals for quantile regression. Recently, Krivobokova et al. (J Am Stat Assoc 105:852–863, 2010 ) provided simultaneous confidence intervals for penalized spline estimator. However, it is well known that the conventional mean-based penalized spline and its confidence intervals collapse when data are not normally distributed such as skewed or heavy-tailed, and hence, the resultant confidence intervals further provide low coverage probability. To overcome this problem, this paper proposes a new approach that constructs simultaneous confidence intervals for penalized quantile spline estimator, which yields a desired coverage probability. The results obtained from numerical experiments and real data validate the effectiveness of the proposed method. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Yaeji Lim & Hee-Seok Oh, 2015. "Simultaneous confidence interval for quantile regression," Computational Statistics, Springer, vol. 30(2), pages 345-358, June.
    • Handle: RePEc:spr:compst:v:30:y:2015:i:2:p:345-358
    DOI: 10.1007/s00180-014-0537-7
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    References listed on IDEAS

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    1. Hee-Seok Oh & Douglas W. Nychka & Thomas C. M. Lee, 2007. "The Role of Pseudo Data for Robust Smoothing with Application to Wavelet Regression," Biometrika, Biometrika Trust, vol. 94(4), pages 893-904.
    2. Krivobokova, Tatyana & Kneib, Thomas & Claeskens, Gerda, 2010. "Simultaneous Confidence Bands for Penalized Spline Estimators," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 852-863.
    3. Fenske, Nora & Kneib, Thomas & Hothorn, Torsten, 2011. "Identifying Risk Factors for Severe Childhood Malnutrition by Boosting Additive Quantile Regression," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 494-510.
    4. Reiss Philip T. & Huang Lei, 2012. "Smoothness Selection for Penalized Quantile Regression Splines," The International Journal of Biostatistics, De Gruyter, vol. 8(1), pages 1-27, May.
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    Cited by:

    1. Italo R. Lima & Guanqun Cao & Nedret Billor, 2019. "M-based simultaneous inference for the mean function of functional data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(3), pages 577-598, June.

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