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Smoothness Selection for Penalized Quantile Regression Splines

Author

Listed:
  • Reiss Philip T.

    (New York University and Nathan Kline Institute)

  • Huang Lei

    (Johns Hopkins University)

Abstract

Modern data-rich analyses may call for fitting a large number of nonparametric quantile regressions. For example, growth charts may be constructed for each of a collection of variables, to identify those for which individuals with a disorder tend to fall in the tails of their age-specific distribution; such variables might serve as developmental biomarkers. When such a large set of analyses are carried out by penalized spline smoothing, reliable automatic selection of the smoothing parameter is particularly important. We show that two popular methods for smoothness selection may tend to overfit when estimating extreme quantiles as a smooth function of a predictor such as age; and that improved results can be obtained by multifold cross-validation or by a novel likelihood approach. A simulation study, and an application to a functional magnetic resonance imaging data set, demonstrate the favorable performance of our methods.

Suggested Citation

  • 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.
    • Handle: RePEc:bpj:ijbist:v:8:y:2012:i:1:n:10
    DOI: 10.1515/1557-4679.1381
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    References listed on IDEAS

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    2. Castiglione, Cristian & Arnone, Eleonora & Bernardi, Mauro & Farcomeni, Alessio & Sangalli, Laura M., 2025. "PDE-regularised spatial quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 205(C).
    3. Yaeji Lim & Hee-Seok Oh, 2015. "Simultaneous confidence interval for quantile regression," Computational Statistics, Springer, vol. 30(2), pages 345-358, June.
    4. Zhang, Likun & Castillo, Enrique del & Berglund, Andrew J. & Tingley, Martin P. & Govind, Nirmal, 2020. "Computing confidence intervals from massive data via penalized quantile smoothing splines," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    5. Qian Yan & Hanyu Li & Chengmei Niu, 2023. "Optimal subsampling for functional quantile regression," Statistical Papers, Springer, vol. 64(6), pages 1943-1968, December.

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