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

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.
M07/02
University of Southampton
Liu, W.
b64150aa-d935-4209-804d-24c1b97e024a
Hayter, A.J.
55bd07a5-db1d-4d3d-8c87-b307485420d9
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.

Record type: 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

Identifiers

Local EPrints ID: 44608
URI: http://eprints.soton.ac.uk/id/eprint/44608
PURE UUID: af2112e5-428e-4890-9e87-fab3e2dcc73c
ORCID for W. Liu: ORCID iD orcid.org/0000-0002-4719-0345

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Date deposited: 28 Feb 2007
Last modified: 16 Mar 2024 02:42

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Contributors

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

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