Minimum area confidence set optimality for confidence bands in simple linear regression
Minimum area confidence set optimality for confidence bands in simple linear regression
The average width of a simultaneous confidence band has been used by several authors (e.g., Naiman and Piegorsch) as a criterion for the comparison of different confidence bands. In this article the area of the confidence set that corresponds 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 and 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.
confidence bands, confidence sets, probability inequalities, minimum area, simple linear regression
181-190
Liu, W.
b64150aa-d935-4209-804d-24c1b97e024a
Hayter, A.J.
55bd07a5-db1d-4d3d-8c87-b307485420d9
March 2007
Liu, W.
b64150aa-d935-4209-804d-24c1b97e024a
Hayter, A.J.
55bd07a5-db1d-4d3d-8c87-b307485420d9
Liu, W. and Hayter, A.J.
(2007)
Minimum area confidence set optimality for confidence bands in simple linear regression.
Journal of the American Statistical Association, 102 (477), .
(doi:10.1198/016214506000001301).
Abstract
The average width of a simultaneous confidence band has been used by several authors (e.g., Naiman and Piegorsch) as a criterion for the comparison of different confidence bands. In this article the area of the confidence set that corresponds 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 and 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: March 2007
Keywords:
confidence bands, confidence sets, probability inequalities, minimum area, simple linear regression
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Local EPrints ID: 46722
URI: http://eprints.soton.ac.uk/id/eprint/46722
ISSN: 0162-1459
PURE UUID: e3cdac0c-491b-43e2-bdcb-f21baebf4a2c
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Date deposited: 19 Jul 2007
Last modified: 16 Mar 2024 02:42
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Author:
A.J. Hayter
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