Comparison of powers of a class of tests for multivariate linear hypothesis and independence
type: Item
instance of: scholarly article
title: Comparison of powers of a class of tests for multivariate linear hypothesis and independence
zbMATH Open document ID: 0644.62064
DOI: 10.1016/0047-259X(88)90072-3
author: Yasunori Fujikoshi
published in: Journal of Multivariate Analysis
publication date: 1988-01-01T00:00:00Z
review text: We consider the class C of test statistics \(T=\sum^{p}_{j=1}Q(\ell_ j)\) for testing the multivariate linear hypothesis and independence of two sets of variables. Here Q(\(\ell)\) is a monotone increasing function for \(\ell \geq 0\), \(Q(0)=0\), \(Q'(0)=1\), and has a continuous third order derivative in a neighborhood of \(\ell =0\). This class includes the likelihood ratio test, Lawley-Hotelling trace test and Bartlett-Nanda- Pillai trace test. We compare the local powers of tests on the basis of the asymptotic expansions of their distributions. The differences in the powers of all the tests in C can be explained in terms of \(\gamma =Q''(0)\). The comparisons reveal no uniform superiority properties.
Mathematics Subject Classification ID: 62H15
Mathematics Subject Classification ID: 62H10
Mathematics Subject Classification ID: 62E20
zbMATH DE Number: 4050788
zbMATH Keywords: MANOVA
zbMATH Keywords: power comparisons
zbMATH Keywords: class of test statistics
zbMATH Keywords: asymptotic expansions of powers
zbMATH Keywords: multivariate linear hypothesis
zbMATH Keywords: independence
zbMATH Keywords: likelihood ratio test
zbMATH Keywords: Lawley-Hotelling trace test
zbMATH Keywords: Bartlett-Nanda-Pillai trace test
zbMATH Keywords: local powers
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4050788