Abstract
A modification is given for the method of derivation of the most powerful location and scale invariant test, which was developed by Hajek and Sidak in 1967. The modification is for the case where the null and alternative hypotheses are assumed to be n—dimensional symmetric densities. An application is given to show that it is worthwhile using the modification when possible. For testing the hypothesis of the family of spherical distributions, a uniformly most powerful location and scale invariant test statistic is obtained.
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