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

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  • Tsai, Ming-Tien

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.

Suggested Citation

  • Tsai, Ming-Tien, 2009. "Asymptotically efficient two-sample rank tests for modal directions on spheres," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 445-458, March.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:3:p:445-458
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    References listed on IDEAS

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    1. Thomas P. Hettmansperger, 2002. "A practical affine equivariant multivariate median," Biometrika, Biometrika Trust, vol. 89(4), pages 851-860, December.
    2. Chang, Ted & Tsai, Ming-Tien, 2003. "Asymptotic relative Pitman efficiency in group models," Journal of Multivariate Analysis, Elsevier, vol. 85(2), pages 395-415, May.
    3. Tsai, Ming-Tien & Sen, Pranab Kumar, 2007. "Locally best rotation-invariant rank tests for modal location," Journal of Multivariate Analysis, Elsevier, vol. 98(6), pages 1160-1179, July.
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    Cited by:

    1. Christophe Ley & Yvik Swan & Thomas Verdebout, 2013. "Efficient ANOVA for Directional Data," Working Papers ECARES ECARES 2012-48, ULB -- Universite Libre de Bruxelles.
    2. Christophe Ley & Yvik Swan & Thomas Verdebout, 2017. "Efficient ANOVA for directional data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(1), pages 39-62, February.

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