Rights statement: 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 http://onlinelibrary.wiley.com/doi/10.1111/sjos.12217/abstract This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving.
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Final published version
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
TY - JOUR
T1 - Simultaneous confidence tubes in multivariate linear regression
AU - Liu, Wei
AU - Han, Yang
AU - Wan, Fang
AU - Bretz, Frank
AU - Hayter, Anthony
N1 - 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 http://onlinelibrary.wiley.com/doi/10.1111/sjos.12217/abstract This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving.
PY - 2016/9
Y1 - 2016/9
N2 - 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.
AB - 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.
KW - multivariate linear regression
KW - multivariate normal distribution
KW - simultaneous confidence band
KW - simultaneous confidence tube
KW - statistical inference
KW - statistical simulation
KW - Wishart distribution
U2 - 10.1111/sjos.12217
DO - 10.1111/sjos.12217
M3 - Journal article
VL - 43
SP - 879
EP - 885
JO - Scandinavian Journal of Statistics
JF - Scandinavian Journal of Statistics
SN - 0303-6898
IS - 3
ER -