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Asymptotic efficiency of some nonparametric tests for location on hyperspheres

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  • Dabo-Niang, Sophie
  • Thiam, Baba
  • Verdebout, Thomas

Abstract

In the present paper, we show that several classical nonparametric tests for multivariate location in the Euclidean case can be adapted to nonparametric tests for the location problem on hyperspheres. The tests we consider are spatial signed-rank tests for location on hyperspheres. We compute the asymptotic powers of the latter tests in the classical rotationally symmetric case. In particular, we show that the spatial signed-rank test uniformly dominates the spatial sign test and has performances that are extremely close to the asymptotically optimal test in the well-known von Mises–Fisher case. Monte-Carlo simulations confirm our asymptotic results.

Suggested Citation

  • Dabo-Niang, Sophie & Thiam, Baba & Verdebout, Thomas, 2022. "Asymptotic efficiency of some nonparametric tests for location on hyperspheres," Statistics & Probability Letters, Elsevier, vol. 188(C).
    • Handle: RePEc:eee:stapro:v:188:y:2022:i:c:s0167715222000979
    DOI: 10.1016/j.spl.2022.109524
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    References listed on IDEAS

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    1. T. Hayakawa, 1990. "On tests for the mean direction of the Langevin distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(2), pages 359-373, June.
    2. Eduardo Garcia-Portugues & Davy Paindaveine & Thomas Verdebout, 2020. "On optimal tests for rotational symmetry against new classes of hyperspherical distributions," Post-Print hal-03169388, HAL.
    3. Ko, D. J. & Chang, T., 1993. "Robust M-Estimators on Spheres," Journal of Multivariate Analysis, Elsevier, vol. 45(1), pages 104-136, April.
    4. Eduardo García-Portugués & Davy Paindaveine & Thomas Verdebout, 2020. "On Optimal Tests for Rotational Symmetry Against New Classes of Hyperspherical Distributions," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(532), pages 1873-1887, December.
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