Bivariate quantile smoothing splines

Xuming He, Pin T Ng, Stephen Portnoy

Research output: Contribution to journalArticle

68 Citations (Scopus)

Abstract

It has long been recognized that the mean provides an inadequate summary whereas the set of quantiles can supply a more complete description of a sample. We introduce bivariate quantile smoothing splines, which belong to the space of bilinear tensor product splines, as non-parametric estimators for the conditional quantile functions in a two-dimensional design space. The estimators can be computed by using standard linear programming techniques and can further be used as building-blocks for conditional quantile estimations in higher dimensions. For moderately large data sets, we recommend penalized bivariate B-splines as approximate solutions. We use real and simulated data to illustrate the methodology proposed.

Original languageEnglish (US)
Pages (from-to)537-550
Number of pages14
JournalJournal of the Royal Statistical Society. Series B: Statistical Methodology
Volume60
Issue number3
StatePublished - 1998
Externally publishedYes

Fingerprint

Conditional Quantiles
Smoothing Splines
Quantile
Tensor Product Splines
Quantile Estimation
Quantile Function
Nonparametric Estimator
B-spline
Large Data Sets
Building Blocks
Higher Dimensions
Linear programming
Approximate Solution
Estimator
Methodology
Conditional quantiles
Smoothing splines
Design
Standards
Splines

Keywords

  • Conditional quantile
  • Linear program
  • Nonparametric regression
  • Robust regression
  • Schwarz information criterion
  • Tensor product spline

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability

Cite this

Bivariate quantile smoothing splines. / He, Xuming; Ng, Pin T; Portnoy, Stephen.

In: Journal of the Royal Statistical Society. Series B: Statistical Methodology, Vol. 60, No. 3, 1998, p. 537-550.

Research output: Contribution to journalArticle

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