Simultaneous confidence tubes for comparing several multivariate linear regression models
Simultaneous confidence tubes for comparing several multivariate linear regression models
Much of the research on multiple comparison and simultaneous inference in the past 60 years or so has been for the comparisons of several population means. Spurrier seems to have been the first to investigate multiple comparisons of several simple linear regression lines using simultaneous confidence bands. In this paper, we extend the work of Liu et al. for finite comparisons of several univariate linear regression models using simultaneous confidence bands to finite comparisons of several multivariate linear regression models using simultaneous confidence tubes. We show how simultaneous confidence tubes can be constructed to allow more informative inferences for the comparison of several multivariate linear regression models than the current approach of hypotheses testing. The methods are illustrated with examples.
multiple comparisons, multivariate linear regression, simultaneous confidence bands, simultaneous inference, statistical simulation
1-13
Peng, Jianan
9842825e-cd6c-41f9-99b5-ea5e9644263c
Liu, Wei
b64150aa-d935-4209-804d-24c1b97e024a
Bretz, Frank
aa8a675f-f53f-4c50-8931-8e9b7febd9f0
Hayter, A.J.
55bd07a5-db1d-4d3d-8c87-b307485420d9
2021
Peng, Jianan
9842825e-cd6c-41f9-99b5-ea5e9644263c
Liu, Wei
b64150aa-d935-4209-804d-24c1b97e024a
Bretz, Frank
aa8a675f-f53f-4c50-8931-8e9b7febd9f0
Hayter, A.J.
55bd07a5-db1d-4d3d-8c87-b307485420d9
Peng, Jianan, Liu, Wei, Bretz, Frank and Hayter, A.J.
(2021)
Simultaneous confidence tubes for comparing several multivariate linear regression models.
Biometrical Journal, .
(doi:10.1002/bimj.202000148).
Abstract
Much of the research on multiple comparison and simultaneous inference in the past 60 years or so has been for the comparisons of several population means. Spurrier seems to have been the first to investigate multiple comparisons of several simple linear regression lines using simultaneous confidence bands. In this paper, we extend the work of Liu et al. for finite comparisons of several univariate linear regression models using simultaneous confidence bands to finite comparisons of several multivariate linear regression models using simultaneous confidence tubes. We show how simultaneous confidence tubes can be constructed to allow more informative inferences for the comparison of several multivariate linear regression models than the current approach of hypotheses testing. The methods are illustrated with examples.
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Accepted/In Press date: 21 January 2021
Published date: 2021
Additional Information:
Funding Information:
We are grateful to the AE and two referees' constructive comments. The first author's research was partially supported by NSERC of Canada.
Publisher Copyright:
© 2021 Wiley-VCH GmbH
Keywords:
multiple comparisons, multivariate linear regression, simultaneous confidence bands, simultaneous inference, statistical simulation
Identifiers
Local EPrints ID: 446843
URI: http://eprints.soton.ac.uk/id/eprint/446843
ISSN: 0323-3847
PURE UUID: 10899591-396a-4eca-b3f4-20edcdc34637
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Date deposited: 24 Feb 2021 17:31
Last modified: 17 Mar 2024 02:37
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Contributors
Author:
Jianan Peng
Author:
Frank Bretz
Author:
A.J. Hayter
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