On the power of Wilks' U-test for MANOVA

Somesh Das Gupta and Michael D. Perlman

Journal of Multivariate Analysis, 1973, vol. 3, issue 2, 220-225

Abstract: Let V1,..., Vm, W1,..., Wn be independent p - 1 random vectors having multivariate normal distributions with common nonsingular covariance matrix [Sigma] and with EW[alpha] = 0, [alpha] = 1,..., n. In this canonical form of the multivariate linear model, the problem is to test H: EV[alpha] az [mu][alpha] = 0, [alpha] = 1,..., m vs K: not H. It is shown that when the rank of the noncentrality matrix ([mu]1...[mu]m) [Sigma]-1 ([mu]1...[mu]m) is one, the power of Wilks' U-test (the likelihood ratio test) strictly decreases with the dimension p and the hypothesis degrees of freedom m. This generalizes results known for the noncentral F-test in the univariate case.

Keywords: MANOVA; power; of; Wilks'; U-test; product; of; beta; variates; monotone; likelihood; ratio; Neyman-Pearson; lemma (search for similar items in EconPapers)
Date: 1973
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Citations: View citations in EconPapers (2)

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