A strictly distribution-free test has been proposed for testing that several independent pairs of random variables have locations as specified. Under the null hypothesis, the test statistic has asymptotically a chi-square distribution with degrees of freedom two. The test has been shown to be unbiased and consistent against reasonable classes of alternatives. Asymptotic power and efficiency have been examined.
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Shoutir Kishore Chatterjee (1966) studied this question.
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