Abstract
In the usual two-sample scale problem it is assumed that the two populations have a common median. We consider the case where the common quantile may be other than a half. We investigate a quite general class, all members are based on U-statistics where the minima and maxima of subsamples of various sizes are used. The asymptotic efficacies are investigated in detail. We construct an adaptive test where all statistics involved are suitably chosen. It is shown that the proposed adaptive test has good asymptotic and finite power properties.
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