Asymptotically efficient two-sample rank tests for modal directions on spheres


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.62H11 62H15 Directional and axial data Optimal spherical rank test Randomly weighted spherical distance Rotation-equivariance Spherical Wilcoxon rank test

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Research Papers in Economics

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Last time updated on 7/6/2012

This paper was published in Research Papers in Economics.

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