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Minimum area confidence set optimality for confidence bands in simple linear regression

Liu, W. and Hayter, A.J. (2007) Minimum area confidence set optimality for confidence bands in simple linear regression , Southampton, GB University of Southampton 30pp. (S3RI Methodology Working Papers, M07/02).

Record type: Monograph (Working Paper)


The average width of a simultaneous confidence band has been used by several authors (e.g. Naiman, 1983, 1984, Piegorsch, 1985a) as a criterion for the comparison of different confidence bands. In this paper, the area of the confidence set corresponding to a confidence band is used as a new criterion. For simple linear regression, comparisons have been carried out under this new criterion between hyperbolic bands, two-segment bands, and three-segment bands, which include constant width bands as special cases. It is found that if one requires a confidence band over the whole range of the covariate, then the best confidence band is given by the Working & Hotelling hyperbolic band. Furthermore, if one needs a confidence band over a finite interval of the covariate, then a restricted hyperbolic band can again be recommended, although a three-segment band may be very slightly superior in certain cases.

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Published date: 28 February 2007


Local EPrints ID: 44608
PURE UUID: af2112e5-428e-4890-9e87-fab3e2dcc73c
ORCID for W. Liu: ORCID iD

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Date deposited: 28 Feb 2007
Last modified: 17 Jul 2017 15:14

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Author: W. Liu ORCID iD
Author: A.J. Hayter

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