Joint Estimation of Quantile Planes Over Arbitrary Predictor Spaces

Yun Yang, Surya T. Tokdar

Research output: Contribution to journalArticlepeer-review


In spite of the recent surge of interest in quantile regression, joint estimation of linear quantile planes remains a great challenge in statistics and econometrics. We propose a novel parameterization that characterizes any collection of noncrossing quantile planes over arbitrarily shaped convex predictor domains in any dimension by means of unconstrained scalar, vector and function valued parameters. Statistical models based on this parameterization inherit a fast computation of the likelihood function, enabling penalized likelihood or Bayesian approaches to model fitting. We introduce a complete Bayesian methodology by using Gaussian process prior distributions on the function valued parameters and develop a robust and efficient Markov chain Monte Carlo parameter estimation. The resulting method is shown to offer posterior consistency under mild tail and regularity conditions. We present several illustrative examples where the new method is compared against existing approaches and is found to offer better accuracy, coverage and model fit. Supplementary materials for this article are available online.

Original languageEnglish (US)
Pages (from-to)1107-1120
Number of pages14
JournalJournal of the American Statistical Association
Issue number519
StatePublished - Jul 3 2017
Externally publishedYes


  • Bayesian inference
  • Bayesian nonparametric models
  • Gaussian processes
  • Joint quantile model
  • Linear quantile regression

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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