Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1146770 | Journal of Multivariate Analysis | 2009 | 14 Pages |
A general class of optimal and distribution-free rank tests for the two-sample modal directions problem on (hyper-) spheres is proposed, along with an asymptotic distribution theory for such spherical rank tests. The asymptotic optimality of the spherical rank tests in terms of power-equivalence to the spherical likelihood ratio tests is studied, while the spherical Wilcoxon rank test, an important case for the class of spherical rank tests, is further investigated. A data set is reanalyzed and some errors made in previous studies are corrected. On the usual sphere, a lower bound on the asymptotic Pitman relative efficiency relative to Hotelling’s T2T2-type test is established, and a new distribution for which the spherical Wilcoxon rank test is optimal is also introduced.