Abstract
The limiting joint distribution of correlated Hotelling’s T 2 statistics associated with multiple comparisons with a control in multivariate one-way layout model is a multivariate central nonsingular chi-square distribution with one-factorial correlation matrix, which has the distribution function expressed in a closed form as an integral of a product of noncentral chi-square distribution functions with respect to a central chi-square density function. For pairwise comparisons, it is a multivariate central singular chi-square distribution whose distribution function is generally intricate. To overcome the complexity of the (exact or asymptotic) distribution theory of \(T^2_{\rm max}\) -type statistics appeared in simultaneous confidence intervals of mean vectors, improved Bonferroni-type inequalities are applied to construct asymptotically conservative simultaneous confidence intervals for pairwise comparisons as well as comparisons with a control.
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Kakizawa, Y. Multiple comparisons of several homoscedastic multivariate populations. Ann Inst Stat Math 61, 1–26 (2009). https://doi.org/10.1007/s10463-007-0134-4
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DOI: https://doi.org/10.1007/s10463-007-0134-4