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\footnotesize
\noindent Statistica Sinica {\bf 16}(2006), 255-266

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\centerline{\large\bf TESTS WITH OPTIMAL AVERAGE POWER IN}
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\centerline{\large\bf  MULTIVARIATE ANALYSIS}
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\author{Samuel S. Wu, Hongying Li and George Casella}
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\centerline{\it University of Florida}
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\noindent {\it Abstract:}
It is well known that in a general multi-parameter setting, there
may not exist any unique best test. More importantly, unlike the
univariate case, the power of different test procedures could vary
remarkably. In this article we extend results of Hsu (1945) and
introduce a new class of tests that have best average power for
multivariate linear hypotheses. A simple method to implement the new
tests is also provided.\par
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\noindent {\it Key words and phrases:}
Average power, multivariate linear hypotheses,
multivariate location problem, Fisher's method of combining tests,
$U$ distribution.\par
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