Simultaneous confidence tubes in multivariate linear regression
Simultaneous confidence tubes in multivariate linear regression
Simultaneous confidence bands have been shown in the statistical literature as powerful inferential tools in univariate linear regression. While the methodology of simultaneous confidence bands for univariate linear regression has been extensively researched and well developed, no published work seems available for multivariate linear regression. This paper fills this gap by studying one particular simultaneous confidence band for multivariate linear regression. Because of the shape of the band, the word ‘tube’ is more pertinent and so will be used to replace the word ‘band’. It is shown that the construction of the tube is related to the distribution of the largest eigenvalue. A simulation‐based method is proposed to compute the 1 − α quantile of this eigenvalue. With the computation power of modern computers, the simultaneous confidence tube can be computed fast and accurately. A real‐data example is used to illustrate the method, and many potential research problems have been pointed out.
879-885
Liu, W.
b64150aa-d935-4209-804d-24c1b97e024a
Han, Y.
7ff3e82b-2df8-40df-adb9-1e0afb985a86
Wan, F.
7cca9739-c6b8-4679-9ba6-94c1ab7c6b6e
Bretz, F.
51270819-e491-4a72-a410-679d86231e64
Hayter, A.J.
55bd07a5-db1d-4d3d-8c87-b307485420d9
September 2016
Liu, W.
b64150aa-d935-4209-804d-24c1b97e024a
Han, Y.
7ff3e82b-2df8-40df-adb9-1e0afb985a86
Wan, F.
7cca9739-c6b8-4679-9ba6-94c1ab7c6b6e
Bretz, F.
51270819-e491-4a72-a410-679d86231e64
Hayter, A.J.
55bd07a5-db1d-4d3d-8c87-b307485420d9
Liu, W., Han, Y., Wan, F., Bretz, F. and Hayter, A.J.
(2016)
Simultaneous confidence tubes in multivariate linear regression.
Scandinavian Journal of Statistics, 43 (3), .
(doi:10.1111/sjos.12217).
Abstract
Simultaneous confidence bands have been shown in the statistical literature as powerful inferential tools in univariate linear regression. While the methodology of simultaneous confidence bands for univariate linear regression has been extensively researched and well developed, no published work seems available for multivariate linear regression. This paper fills this gap by studying one particular simultaneous confidence band for multivariate linear regression. Because of the shape of the band, the word ‘tube’ is more pertinent and so will be used to replace the word ‘band’. It is shown that the construction of the tube is related to the distribution of the largest eigenvalue. A simulation‐based method is proposed to compute the 1 − α quantile of this eigenvalue. With the computation power of modern computers, the simultaneous confidence tube can be computed fast and accurately. A real‐data example is used to illustrate the method, and many potential research problems have been pointed out.
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Accepted/In Press date: 15 December 2015
e-pub ahead of print date: 16 March 2016
Published date: September 2016
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Statistics
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Local EPrints ID: 390358
URI: http://eprints.soton.ac.uk/id/eprint/390358
ISSN: 0303-6898
PURE UUID: f6ff8ed6-1e4a-4f14-a681-dd133b7ad96e
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Date deposited: 24 Mar 2016 13:58
Last modified: 15 Mar 2024 05:27
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Author:
Y. Han
Author:
F. Wan
Author:
F. Bretz
Author:
A.J. Hayter
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