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December, 1963 Minimax Character of Hotelling's $T^2$ Test in the Simplest Case
N. Giri, J. Kiefer, C. Stein
Ann. Math. Statist. 34(4): 1524-1535 (December, 1963). DOI: 10.1214/aoms/1177703884


In the first nontrivial case, dimension $p = 2$ and sample size $N = 3$, it is proved that Hotelling's $T^2$ test of level $\alpha$ maximizes, among all level $\alpha$ tests, the minimum power on each of the usual contours where the $T^2$ test has constant power. A corollary is that the $T^2$ test is most stringent of level $\alpha$ in this case.


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N. Giri. J. Kiefer. C. Stein. "Minimax Character of Hotelling's $T^2$ Test in the Simplest Case." Ann. Math. Statist. 34 (4) 1524 - 1535, December, 1963.


Published: December, 1963
First available in Project Euclid: 27 April 2007

zbMATH: 0202.49506
MathSciNet: MR156408
Digital Object Identifier: 10.1214/aoms/1177703884

Rights: Copyright © 1963 Institute of Mathematical Statistics

Vol.34 • No. 4 • December, 1963
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