Simultaneous Confidence Tubes in Multivariate Linear Regression

Wei Liu, Yang Han, Fang Wan, Frank Bretz, Anthony J. Hayter

    Research output: Contribution to journalArticlepeer-review


    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.
    Manchester University
    Original languageEnglish
    Pages (from-to)879-885
    JournalScandinavian Journal of Statistics
    Issue number3
    Early online date17 Mar 2016
    Publication statusPublished - Sept 2016


    • multivariate linear regression
    • multivariate normal distribution
    • simultaneous confidence band
    • simultaneous confidence tube
    • statistical inference
    • statistical simulation
    • Wishart distribution


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