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

Record type: Article

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.

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Citation

Liu, W., Jamshidian, M., Zhang, Y. and Donnelly, J. (2005) Simulation-based simultaneous confidence bands in multiple linear regression with predictor variables constrained in intervals Journal of Computational and Graphical Statistics, 14, (2), pp. 459-484. (doi:10.1198/106186005X47408).

More information

Published date: June 2005
Keywords: inequality constraints, linear regression, polyhedral cone, projection, quadratic programming, statistical simulation
Organisations: Statistics

Identifiers

Local EPrints ID: 30122
URI: http://eprints.soton.ac.uk/id/eprint/30122
ISSN: 1061-8600
PURE UUID: 58239aa0-6b5f-4853-a6aa-dd1718d18b12
ORCID for W. Liu: ORCID iD orcid.org/0000-0002-4719-0345

Catalogue record

Date deposited: 12 May 2006
Last modified: 17 Jul 2017 15:55

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Contributors

Author: W. Liu ORCID iD
Author: M. Jamshidian
Author: Y. Zhang
Author: J. Donnelly

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