Simultaneous confidence tubes in multivariate linear regression

Liu, Wei and Han, Yang and Wan, Fang and Bretz, Frank and Hayter, Anthony (2016) Simultaneous confidence tubes in multivariate linear regression. Scandinavian Journal of Statistics, 43 (3). pp. 879-885. ISSN 0303-6898

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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.

Item Type:
Journal Article
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Scandinavian Journal of Statistics
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This is the peer reviewed version of the following article: Liu, W., Han, Y., Wan, F., Bretz, F., and Hayter, A. J. (2016) Simultaneous Confidence Tubes in Multivariate Linear Regression. Scand J Statist, 43: 879–885. doi: 10.1111/sjos.12217 which has been published in final form at This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving.
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13 Apr 2016 10:32
Last Modified:
09 Aug 2022 00:06