Comparison of powers of a class of tests for multivariate linear hypothesis and independence
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.
scientific article; zbMATH DE number 4050788
scientific article