## The Annals of Statistics

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

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

#### 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