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, 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.
University of Southampton
Liu, W.
b64150aa-d935-4209-804d-24c1b97e024a
Hayter, A.J.
55bd07a5-db1d-4d3d-8c87-b307485420d9
28 February 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
(S3RI Methodology Working Papers, M07/02)
Southampton, GB.
University of Southampton
30pp.
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Monograph
(Working Paper)
Abstract
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
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Local EPrints ID: 44608
URI: http://eprints.soton.ac.uk/id/eprint/44608
PURE UUID: af2112e5-428e-4890-9e87-fab3e2dcc73c
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Date deposited: 28 Feb 2007
Last modified: 16 Mar 2024 02:42
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Author:
A.J. Hayter
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