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The International Journal of Biostatistics

Ed. by Chambaz, Antoine / Hubbard, Alan E. / van der Laan, Mark J.

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Smoothness Selection for Penalized Quantile Regression Splines

Philip T. Reiss
  • New York University and Nathan Kline Institute
/ Lei Huang
  • Johns Hopkins University
Published Online: 2012-05-16 | DOI: https://doi.org/10.1515/1557-4679.1381

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.

Keywords: asymmetric Laplace distribution; functional connectivity; generalized approximate cross-validation; growth chart; nonparametric quantile regression; smoothing parameter

About the article

Published Online: 2012-05-16

Citation Information: The International Journal of Biostatistics, ISSN (Online) 1557-4679, DOI: https://doi.org/10.1515/1557-4679.1381. Export Citation

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