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On the power of Wilks' U-test for MANOVA

Author

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  • Gupta, Somesh Das
  • Perlman, Michael D.

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.

Suggested Citation

  • Gupta, Somesh Das & Perlman, Michael D., 1973. "On the power of Wilks' U-test for MANOVA," Journal of Multivariate Analysis, Elsevier, vol. 3(2), pages 220-225, June.
    • Handle: RePEc:eee:jmvana:v:3:y:1973:i:2:p:220-225
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    Cited by:

    1. Bhaumik, Dulal Kumar & Sarka, Sanat K., 2002. "On the Power Function of the Likelihood Ratio Test for MANOVA," Journal of Multivariate Analysis, Elsevier, vol. 82(2), pages 416-421, August.
    2. Luis Rodriguez-Carvajal, 1999. "Multivariate AB-BA crossover trial," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(3), pages 393-403.

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