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