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Local Powers of Optimal One-sample and Multi-sample Tests for the Concentration of Fisher-von Mises-Langevin Distributions

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  • Christophe Ley
  • Thomas Verdebout

Abstract

type="main" xml:id="insr12047-abs-0001"> One-sample and multi-sample tests on the concentration parameter of Fisher-von Mises-Langevin distributions on (hyper-)spheres have been well studied in the literature. However, only little is known about their behaviour under local alternatives, which is due to complications inherent to the curved nature of the parameter space. The aim of the present paper therefore consists in filling that gap by having recourse to the Le Cam methodology, which has recently been adapted from the linear to the spherical setup. We obtain explicit expressions of the powers for the most efficient one- and multi-sample tests. As a nice by-product, we are also able to write down the powers (against local Fisher-von Mises-Langevin alternatives) of the celebrated Rayleigh test of uniformity. A Monte Carlo simulation study confirms our theoretical findings and shows the empirical powers of the above-mentioned procedures.

Suggested Citation

  • Christophe Ley & Thomas Verdebout, 2014. "Local Powers of Optimal One-sample and Multi-sample Tests for the Concentration of Fisher-von Mises-Langevin Distributions," International Statistical Review, International Statistical Institute, vol. 82(3), pages 440-456, December.
    • Handle: RePEc:bla:istatr:v:82:y:2014:i:3:p:440-456
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    File URL: http://hdl.handle.net/10.1111/insr.12047
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    References listed on IDEAS

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    1. P. V. Larsen, 2002. "Improved likelihood ratio tests on the von Mises--Fisher distribution," Biometrika, Biometrika Trust, vol. 89(4), pages 947-951, December.
    2. repec:eca:wpaper:2013/122336 is not listed on IDEAS
    3. Watamori, Yoko & Jupp, Peter E., 2005. "Improved likelihood ratio and score tests on concentration parameters of von Mises-Fisher distributions," Statistics & Probability Letters, Elsevier, vol. 72(2), pages 93-102, April.
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    Cited by:

    1. Ley, Christophe & Verdebout, Thomas, 2017. "Skew-rotationally-symmetric distributions and related efficient inferential procedures," Journal of Multivariate Analysis, Elsevier, vol. 159(C), pages 67-81.
    2. Aboubacar Amiri & Baba Thiam & Thomas Verdebout, 2017. "On the Estimation of the Density of a Directional Data Stream," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(1), pages 249-267, March.
    3. Christophe Ley & Thomas Verdebout, 2014. "Skew-rotsymmetric Distributions on Unit Spheres and Related Efficient Inferential Proceedures," Working Papers ECARES ECARES 2014-46, ULB -- Universite Libre de Bruxelles.

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