Asymptotically efficient two-sample rank tests for modal directions on spheres |
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Authors: | Ming-Tien Tsai |
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Institution: | Institute of Statistical Science, Academia Sinica, Taipei 11529, Taiwan, ROC |
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Abstract: | 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 T2-type test is established, and a new distribution for which the spherical Wilcoxon rank test is optimal is also introduced. |
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Keywords: | 62H11 62H15 |
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