W. Kossler et H. Buning, The asymptotic power and relative efficiency of some c-sample rank tests of homogeneity against umbrella alternatives, STATISTICS, 34(1), 2000, pp. 1-26
For the c-sample location problem with umbrella alternatives we compare som
e generalizations of the test of Mack and Wolfe (1981). All the tests are b
ased on pairwise ranking methods. The asymptotic power and asymptotic relat
ive efficiency of the so-called Mack-Wolfe-type test, Tryon-Hettmannsperger
-type-test and Purl-type test are derived and compared with modifications o
f the test of Hettmansperger and Norton (1987) where the ranks are taken ov
er all samples.
The Mack-Wolfe-type test and the Tryon-Hettmansperger-type-test are further
generalized by introducing weight coefficients for the substatistics. For
the case of a specified alternative these weights are determined in such a
way that the efficacies become maximal. It is shown that the maximal achiev
able efficacies in the defined classes of the generalized Mack-Wolfe-type t
est and Tryon-Hettmansperger-type test always are equal.
The case of an unknown peak is briefly discussed.