Smoothness selection for penalized quantile regression splines

Philip T. Reiss, Lei Huang

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article number1381
JournalInternational Journal of Biostatistics
Issue number1
StatePublished - 2014
Externally publishedYes


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

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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