Simultaneous Interval Estimation in the General Multivariate Analysis of Variance Model

Let M ∈ 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 ∈ Rm, b ∈ Rpand$\operatorname...

Full description

Saved in:
Bibliographic Details
Published in:The Annals of statistics 1983-06, Vol.11 (2), p.666-673
Main Author: Hooper, Peter M.
Format: Article
Language:English
Subjects:
62F25
62J15
Analysis of variance
Confidence interval
confidence intervals
Confidence sets
Eigenvalues
Estimators
exact
growth curves
Index sets
Indicator functions
invariant
MANOVA
Mathematical functions
Mathematical inequalities
Modeling
self-reproducing
step-down procedure
Citations: Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Let M ∈ 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 ∈ Rm, b ∈ Rpand$\operatorname{tr} N'M$for all N ∈ 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.
ISSN:0090-5364
2168-8966
DOI:10.1214/aos/1176346171