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March, 1955 Rank Sum Tests of Fit
Chia Kuei Tsao
Ann. Math. Statist. 26(1): 94-104 (March, 1955). DOI: 10.1214/aoms/1177728596


This paper suggests several `goodness of fit' test criteria, all having a linear form. The moment generating function and the limiting distribution of this linear form are obtained in Section 2. The best test criterion of this form for testing a simple hypothesis $H_0$ against a simple alternative hypothesis $H_1$ is shown, in Section 3, to be in general not independent of $H_1$. The remainder of this paper deals with a special case of the linear form, that is, the rank sum test criterion. The distribution of this test criterion is derived in Section 4, its consistency is proved in Section 5, and some numerical asymptotic efficiencies are calculated in Section 6. Within a certain class of tests, the present test is shown, in Section 7, to be uniformly most powerful for a special family of alternatives.


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Chia Kuei Tsao. "Rank Sum Tests of Fit." Ann. Math. Statist. 26 (1) 94 - 104, March, 1955.


Published: March, 1955
First available in Project Euclid: 28 April 2007

zbMATH: 0065.12102
MathSciNet: MR68788
Digital Object Identifier: 10.1214/aoms/1177728596

Rights: Copyright © 1955 Institute of Mathematical Statistics

Vol.26 • No. 1 • March, 1955
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