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June, 1967 On the Large Sample Properties of a Generalized Wilcoxon-Mann-Whitney Statistic
A. P. Basu
Ann. Math. Statist. 38(3): 905-915 (June, 1967). DOI: 10.1214/aoms/1177698884


Let there be two independent samples of sizes $m$ and $n$ respectively from two populations with continuous cdf's $F(x)$ and $G(y)$. To test the equality of the two populations Sobel [19], has proposed the statistic $V^{m,n}_r$ (to be defined later) based on the first $r$ ordered observations only. In this paper the large sample properties of $V^{m,n}_r$ have been studied. The test is compared with other "$r$ out of $N$" tests by computing the appropriate asymptotic relative efficiencies. The test statistic is found to be quite satisfactory in all the cases considered and is particularly suitable for location alternatives.


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A. P. Basu. "On the Large Sample Properties of a Generalized Wilcoxon-Mann-Whitney Statistic." Ann. Math. Statist. 38 (3) 905 - 915, June, 1967.


Published: June, 1967
First available in Project Euclid: 27 April 2007

zbMATH: 0149.15006
MathSciNet: MR212951
Digital Object Identifier: 10.1214/aoms/1177698884

Rights: Copyright © 1967 Institute of Mathematical Statistics

Vol.38 • No. 3 • June, 1967
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