On the Large Sample Properties of a Generalized Wilcoxon-Mann-Whitney Statistic

Abstract

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.