Abstract
When testing hypotheses on the basis of two-sample linear rank statistics, the standard null hypothesis is that the two samples are from identical populations. In this paper, a method is given for modifying a class of linear rank statistics to obtain statistics appropriate for testing the hypothesis of equal medians when the populations are symmetric but do not necessarily have the same shape. The proposed procedures require consistent rank statistic estimates of the asymptotic variance of the statistics to be modified. These estimates are obtained and their almost sure convergence is established.
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