## Annals of Statistics

### Simultaneous Interval Estimation in the General Multivariate Analysis of Variance Model

Peter M. Hooper

#### Abstract

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 information

Source
Ann. Statist., Volume 11, Number 2 (1983), 666-673.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176346171

Digital Object Identifier
doi:10.1214/aos/1176346171

Mathematical Reviews number (MathSciNet)
MR696077

Zentralblatt MATH identifier
0526.62032

JSTOR