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Biometrika 1972 59(3):649-664; doi:10.1093/biomet/59.3.649
© 1972 by Biometrika Trust
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Some results on the distribution of Wilks's likelihood-ratio criterion

YOONG-SIN LEE*

University of Malaya Kuala Lumpur

*Now at the University of Toronto.

The null distribution of Wilks's likelihood ratio criterion A is examined in its exact and asymptotic forms. The case when p, the number of variates, and q, the number of hypothesis degrees of freedom, are both odd is considered and in this case the distribution is given in simple integral form. The results are used to develop techniques for computing the distribution. Tables of the chi-squared correction factors for the percentage points are extended to cover, in conjunction with existing tables, values for all p {theta} q {theta} 20 and pq {theta} 144 with omission when p or q is odd and greater than 10.

Key Words: Multivariate analysis of variance • Likelihood ratio test statistics • Wilks's test criterion • Beta distribution • Asymptotic formula


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