POWER COMPARISON OF HYPOTHESIS TESTING FOR AN INTERMEDIATE LATENT VECTOR OF COVARIANCE MATRIX

We consider the test of equality of the latent vector and a specified vector. In this paper, we discuss three criteria for testing hypothesis. The test statistic Λ_1 is the inner product of the sample latent vector and the specified vector. The statistic Λ_2 is the α-th factor of some likelihood ratio criterion. The Λ_3 is the statistic given by T. W. Anderson. We calculate the percentiles based on the exact distribution of the statistic Λ_2. To compute the power, we obtained the non-null distribution of the statistic Λ_1, Λ_2 and Λ_3. And we compare the power of test using these three criteria on a bivariate and trivariate normal distribution.