Quantile regression for longitudinal data

Roger Koenker

Research output: Contribution to journalArticlepeer-review


The penalized least squares interpretation of the classical random effects estimator suggests a possible way forward for quantile regression models with a large number of "fixed effects". The introduction of a large number of individual fixed effects can significantly inflate the variability of estimates of other covariate effects. Regularization, or shrinkage of these individual effects toward a common value can help to modify this inflation effect. A general approach to estimating quantile regression models for longitudinal data is proposed employing ℓ1 regularization methods. Sparse linear algebra and interior point methods for solving large linear programs are essential computational tools.

Original languageEnglish (US)
Pages (from-to)74-89
Number of pages16
JournalJournal of Multivariate Analysis
Issue number1
StatePublished - Oct 2004


  • Hierarchical models
  • L-statistics
  • Penalty methods
  • Quantile regression
  • Random effects
  • Robust estimation
  • Shrinkage

ASJC Scopus subject areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty


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