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December, 1964 Minimax Character of the $R^2$-Test in the Simplest Case
N. Giri, J. Kiefer
Ann. Math. Statist. 35(4): 1475-1490 (December, 1964). DOI: 10.1214/aoms/1177700374


In the first nontrivial case, dimension $p = 3$ and sample size $N = 3$ or 4 (depending on whether or not the mean is known), it is proved that the classical level $\alpha$ normal test of independence of the first component from the others, based on the squared sample multiple correlation coefficient $R^2$, maximizes, among all level $\alpha$ tests, the minimum power on each of the usual contours where the $R^2$-test has constant power. A corollary is that the $R^2$-test is most stringent of level $\alpha$ in this case.


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N. Giri. J. Kiefer. "Minimax Character of the $R^2$-Test in the Simplest Case." Ann. Math. Statist. 35 (4) 1475 - 1490, December, 1964.


Published: December, 1964
First available in Project Euclid: 27 April 2007

zbMATH: 0137.36802
MathSciNet: MR169328
Digital Object Identifier: 10.1214/aoms/1177700374

Rights: Copyright © 1964 Institute of Mathematical Statistics

Vol.35 • No. 4 • December, 1964
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