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June, 1983 Simultaneous Interval Estimation in the General Multivariate Analysis of Variance Model
Peter M. Hooper
Ann. Statist. 11(2): 666-673 (June, 1983). DOI: 10.1214/aos/1176346171


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.


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Peter M. Hooper. "Simultaneous Interval Estimation in the General Multivariate Analysis of Variance Model." Ann. Statist. 11 (2) 666 - 673, June, 1983.


Published: June, 1983
First available in Project Euclid: 12 April 2007

zbMATH: 0526.62032
MathSciNet: MR696077
Digital Object Identifier: 10.1214/aos/1176346171

Primary: 62F25
Secondary: 62J15

Keywords: confidence intervals , Confidence sets , exact , growth curves , invariant , MANOVA , self-reproducing , step-down procedure

Rights: Copyright © 1983 Institute of Mathematical Statistics


Vol.11 • No. 2 • June, 1983
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