Annals of Statistics

Simultaneous Interval Estimation in the General Multivariate Analysis of Variance Model

Peter M. Hooper

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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

Permanent link to this document
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
links.jstor.org

Subjects
Primary: 62F25: Tolerance and confidence regions
Secondary: 62J15: Paired and multiple comparisons

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

Citation

Hooper, Peter M. Simultaneous Interval Estimation in the General Multivariate Analysis of Variance Model. Ann. Statist. 11 (1983), no. 2, 666--673. doi:10.1214/aos/1176346171. https://projecteuclid.org/euclid.aos/1176346171


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Corrections

  • See Correction: Peter M. Hooper. Corrections: Simultaneous Interval Estimation in the General Multivariate Analysis of Variance Model. Ann. Statist., Volume 12, Number 2 (1984), 785--785.