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

Ming-Tien Tsai

Journal of Multivariate Analysis, 2009, vol. 100, issue 3, 445-458

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.

Keywords: 62H11; 62H15; Directional; and; axial; data; Optimal; spherical; rank; test; Randomly; weighted; spherical; distance; Rotation-equivariance; Spherical; Wilcoxon; rank; test (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (2)

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