The Annals of Statistics

Admissibility of Invariant Tests in the General Multivariate Analysis of Variance Problem

John I. Marden

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Abstract

Necessary and sufficient conditions for an invariant test to be admissible among invariant tests in the general multivariate analysis of variance problem are presented. It is shown that in many cases the popular tests based on the likelihood ratio matrix are inadmissible. Other tests are shown admissible. Numerical work suggests that the inadmissibility of the likelihood ratio test is not serious. The results are given for the multivariate analysis of variance problem as a special case.

Article information

Source
Ann. Statist., Volume 11, Number 4 (1983), 1086-1099.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176346323

Digital Object Identifier
doi:10.1214/aos/1176346323

Mathematical Reviews number (MathSciNet)
MR720255

Zentralblatt MATH identifier
0598.62006

JSTOR
links.jstor.org

Subjects
Primary: 62C07: Complete class results
Secondary: 62C15: Admissibility 62H15: Hypothesis testing 62H30: Classification and discrimination; cluster analysis [See also 68T10, 91C20] 62J10: Analysis of variance and covariance

Keywords
General multivariate analysis of variance multivariate analysis of variance multivariate normal distribution invariant tests minimal complete class admissible tests Bayes tests likelihood ratio test

Citation

Marden, John I. Admissibility of Invariant Tests in the General Multivariate Analysis of Variance Problem. Ann. Statist. 11 (1983), no. 4, 1086--1099. doi:10.1214/aos/1176346323. https://projecteuclid.org/euclid.aos/1176346323


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