Simulation-based simultaneous confidence bands in multiple linear regression with predictor variables constrained in intervals

W. Liu, M. Jamshidian, Y. Zhang, J. Donnelly

Research output: Contribution to journalArticle

37 Scopus citations

Abstract

This article presents a method for the construction of a simultaneous confidence band for the normal-error multiple linear regression model. The confidence bands considered have their width proportional to the standard error of the estimated regression function, and the predictor variables are allowed to be constrained in intervals. Past articles in this area gave exact bands only for the simple regression model. When there is more than one predictor variable, only conservative bands are proposed in the statistics literature. This article advances this methodology by providing simulation-based confidence bands for regression models with any number of predictor variables. Additionally, a criterion is proposed to assess the sensitivity of a simultaneous confidence band. This criterion is defined to be the probability that a false linear regression model is excluded from the band at least at one point and hence this false linear regression model is correctly declared as a false model by the band. Finally, the article considers and compares several computational algorithms for obtaining the confidence band.

Original languageEnglish (US)
Pages (from-to)459-484
Number of pages26
JournalJournal of Computational and Graphical Statistics
Volume14
Issue number2
DOIs
StatePublished - Jun 1 2005
Externally publishedYes

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Keywords

  • Inequality constraints
  • Linear regression
  • Polyhedral cone
  • Projection
  • Quadratic programming
  • Statistical simulation

ASJC Scopus subject areas

  • Statistics and Probability
  • Discrete Mathematics and Combinatorics
  • Statistics, Probability and Uncertainty

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