On the max u-ratio and likelihood ratio tests of equality of several covariance matrices
Titel:
On the max u-ratio and likelihood ratio tests of equality of several covariance matrices
Auteur:
Pillai, K. C. S. Purdue, Dennis L Young
Verschenen in:
Communications in statistics
Paginering:
Jaargang 3 (1974) nr. 1 pagina's 29-53
Jaar:
1974
Inhoud:
Letπ1,…,πk be k p-variate normal populations with unknown covariance matrices ∑1,…,∑k, respectively. The max U-ratio test statistic proposed by Pillai for testing H0:∑1=…=∑k is investigated first, studying its exact distribution for k=2 amd p=2, and approximations for higher values of k and p, and percentage points are tabulated. Then the distribution of the modified likelihood ratio criterion for testing H0 is considered for the case of k=2 and p=2 and 4 and percentage points tabulated for p=2. The non-null distributions of the two test criteria are found for k=2 and p=2 using zonal polynomials up to the sixth degree. Comparisons are made of the powers of the two tests.
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