Quantile splines with several covariates

Xuming He, Pin T Ng

Research output: Contribution to journalArticle

27 Citations (Scopus)

Abstract

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
Volume75
Issue number2
StatePublished - Jan 1 1999
Externally publishedYes

Fingerprint

Quantile
Splines
Spline
Covariates
Tensor Product Splines
Univariate
Roughness Penalty
Regression Quantiles
Tensors
Spline Functions
Main Effect
Model Selection
Justification
Fidelity
Subspace
Analysis of variance (ANOVA)
Decompose
Approximation
Surface roughness
Interaction

Keywords

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

ASJC Scopus subject areas

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

Cite this

Quantile splines with several covariates. / He, Xuming; Ng, Pin T.

In: Journal of Statistical Planning and Inference, Vol. 75, No. 2, 01.01.1999, p. 343-352.

Research output: Contribution to journalArticle

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