Let $M \in M(m, p)$ be the matrix of means of interest in the GMANOVA problem. Our main results characterize all confidence sets for $M$ in a given class (invariant plus a weak additional restriction) that are exact for the families of parametric functions $a'Mb$ for all $a \in \mathbb{R}^m, b \in \mathbb{R}^p$ and $\operatorname{tr} N'M$ for all $N \in M(m, p)$. The corresponding families of smallest exact simultaneous confidence intervals are also given. Similar results are obtained for the MANOVA problem under triangular group reduction.
@article{1176346171,
author = {Hooper, Peter M.},
title = {Simultaneous Interval Estimation in the General Multivariate Analysis of Variance Model},
journal = {Ann. Statist.},
volume = {11},
number = {1},
year = {1983},
pages = { 666-673},
language = {en},
url = {http://dml.mathdoc.fr/item/1176346171}
}
Hooper, Peter M. Simultaneous Interval Estimation in the General Multivariate Analysis of Variance Model. Ann. Statist., Tome 11 (1983) no. 1, pp. 666-673. http://gdmltest.u-ga.fr/item/1176346171/