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).


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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.

Item Type: Monograph (Working Paper)
Subjects: H Social Sciences > HA Statistics
Divisions : University Structure - Pre August 2011 > Southampton Statistical Sciences Research Institute
ePrint ID: 44608
Accepted Date and Publication Date:
28 February 2007Published
Date Deposited: 28 Feb 2007
Last Modified: 31 Mar 2016 12:18

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