Minimal complete classes of invariant tests for equality of normal covariance matrices and sphericity
type: Item
instance of: scholarly article
title: Minimal complete classes of invariant tests for equality of normal covariance matrices and sphericity
zbMATH Open document ID: 0649.62049
DOI: 10.1016/0047-259X(88)90121-2
author: Arthur Cohen
author: John I. Marden
published in: Journal of Multivariate Analysis
publication date: 1988-01-01T00:00:00Z
review text: The problem of testing equality of two normal covariance matrices, \(\Sigma_ 1=\Sigma_ 2\), is studied. Two alternative hypotheses, \(\Sigma_ 1\neq \Sigma_ 2\) and \(\Sigma_ 1-\Sigma_ 2>0\) are considered. Minimal complete classes among the class of invariant tests are found. The group of transformations leaving the problems invariant is the group of nonsingular matrices. The maximal invariant statistic is the ordered characteristic roots of \(S_ 1S_ 2^{-1}\), where \(S_ i\), \(i=1,2\), are the sample covariance matrices. Several tests based on the largest and smallest roots are proven to be inadmissible. Other tests are examined for admissibility in the class of invariant tests. The problem of testing for sphericity of a normal covariance matrix is also studied. Again a minimal complete class of invariant tests is found. The popular tests are again examined for admissibility and inadmissibility in the class of invariant tests.
Mathematics Subject Classification ID: 62H15
Mathematics Subject Classification ID: 62C07
Mathematics Subject Classification ID: 62A01
zbMATH DE Number: 4060548
zbMATH Keywords: testing equality of two normal covariance matrices
zbMATH Keywords: class of invariant tests
zbMATH Keywords: group of nonsingular matrices
zbMATH Keywords: maximal invariant statistic
zbMATH Keywords: ordered characteristic roots
zbMATH Keywords: testing for sphericity
zbMATH Keywords: minimal complete class of invariant tests
zbMATH Keywords: inadmissibility
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4060548