Quantile splines with several covariates

Xuming He, Pin Ng

Research output: Contribution to journalArticlepeer-review

35 Scopus citations


We extend univariate regression quantile splines to problems with several covariates. We adopt an ANOVA-type decomposition approach with main effects captured by linear splines and second-order 'interactions' modeled by bi-linear tensor-product splines. Both univariate linear splines and bi-linear tensor-product splines are optimal when fidelity to data are balanced by a roughness penalty on the fitted function. The problem of sub-model selection and asymptotic justification for using a smaller sub-space of the spline functions in the approximation are discussed. Two examples are considered to illustrate the empirical performance of the proposed methods.

Original languageEnglish (US)
Pages (from-to)343-352
Number of pages10
JournalJournal of Statistical Planning and Inference
Issue number2
StatePublished - Jan 1 1999


  • 62G07
  • Information criterion
  • Linear program
  • Model selection
  • Nonparametric regression
  • Regression quantiles
  • Smoothing
  • Tensor-product spline

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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