On Comparisons of Exact Powers of Bivariate GMANOVA Tests

Abstract

Exact powers of four classical tests in a GMANOVA model are compared numerically when the order of the error sum of square matrix is 2. The four tests are likelihood ratio (=LR), Pillai's V, Hotelling's T ², and Roy's largest root tests. It turns out that for small sizes, there are a few cases in which Rothenberg's condition for the relative magnitude of asymptotic powers of three standard tests does not hold.

Keywords:

• Classical tests in a GMANOVA model
• Hypergeometric function of matrix argument
• Laguerre polynomials of matrix argument
• Mellin transform
• Rothenberg's condition
• Zonal polynomials

Mathematics Subject Classification:

• Primary 62H15
• Secondary 62J12

Acknowledgments

The author would like to thank the referees and associate editor for their kind and helpful comments and Professor Takakazu Sugiyama for his encouragements. In addition, I am grateful to Professor Nariaki Sugiura and Yasunori Fujikoshi for their useful and kind advice and encouragement.