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. Journal of the American Statistical Association, 102, (477), 181-190. (doi:10.1198/016214506000001301).
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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.
|Keywords:||confidence bands, confidence sets, probability inequalities, minimum area, simple linear regression|
|Subjects:||Q Science > QA Mathematics
H Social Sciences > HA Statistics
|Divisions:||University Structure - Pre August 2011 > Southampton Statistical Sciences Research Institute
|Date Deposited:||19 Jul 2007|
|Last Modified:||01 Jun 2011 02:23|
|Contact Email Address:||W.Liu@maths.soton.ac.uk|
|RDF:||RDF+N-Triples, RDF+N3, RDF+XML, Browse.|
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