Simultaneous confidence bands in linear modelling
Simultaneous confidence bands in linear modelling
Constructing simultaneous confidence bands in regression has a history dating back to Working and Hotelling (1929). In general though bands with exact confidence levels were only available in certain special cases. Bands which have exact confidence over any restricted range of the explanatory variables are constructed here. Exact one-sided bands are also constructed. An investigation into the power of these bands when used as a testing procedure to decide if a surface could be the underlying model is also carried out, with results which show this procedure may perform better in certain cases than the F-test, though in other cases the F-test fared better (Scheffé (1959)).
Prediction was also looked at from a simultaneous perspective, but here the results obtained were not very promising.
University of Southampton
2003
Donnelly, Jonathan H. M
(2003)
Simultaneous confidence bands in linear modelling.
University of Southampton, Doctoral Thesis.
Record type:
Thesis
(Doctoral)
Abstract
Constructing simultaneous confidence bands in regression has a history dating back to Working and Hotelling (1929). In general though bands with exact confidence levels were only available in certain special cases. Bands which have exact confidence over any restricted range of the explanatory variables are constructed here. Exact one-sided bands are also constructed. An investigation into the power of these bands when used as a testing procedure to decide if a surface could be the underlying model is also carried out, with results which show this procedure may perform better in certain cases than the F-test, though in other cases the F-test fared better (Scheffé (1959)).
Prediction was also looked at from a simultaneous perspective, but here the results obtained were not very promising.
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Published date: 2003
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Local EPrints ID: 465122
URI: http://eprints.soton.ac.uk/id/eprint/465122
PURE UUID: 40e8d30e-cdae-484c-87dd-afc9cb00cbbf
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Date deposited: 05 Jul 2022 00:24
Last modified: 05 Jul 2022 00:24
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Author:
Jonathan H. M Donnelly
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