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Tests of Concentration for Low-Dimensional and High-Dimensional Directional Data

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  • Christine Cutting
  • Davy Paindaveine
  • Thomas Verdebout

Abstract

We consider asymptotic inference for the concentration of directional data. More precisely, wepropose tests for concentration (i) in the low-dimensional case where the sample size n goes to infinity andthe dimension p remains fixed, and (ii) in the high-dimensional case where both n and p become arbitrarilylarge. To the best of our knowledge, the tests we provide are the first procedures for concentration thatare valid in the (n; p)-asymptotic framework. Throughout, we consider parametric FvML tests, that areguaranteed to meet asymptotically the nominal level constraint under FvML distributions only, as well as“pseudo-FvML” versions of such tests, that are validity-robust within the class of rotationally symmetricdistributions.We conduct a Monte-Carlo study to check our asymptotic results and to investigate the finitesamplebehavior of the proposed tests.

Suggested Citation

  • Christine Cutting & Davy Paindaveine & Thomas Verdebout, 2015. "Tests of Concentration for Low-Dimensional and High-Dimensional Directional Data," Working Papers ECARES ECARES 2015-05, ULB -- Universite Libre de Bruxelles.
  • Handle: RePEc:eca:wpaper:2013/194991
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    References listed on IDEAS

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    1. Tony Cai, T. & Jiang, Tiefeng, 2012. "Phase transition in limiting distributions of coherence of high-dimensional random matrices," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 24-39.
    2. Ley, Christophe & Paindaveine, Davy & Verdebout, Thomas, 2015. "High-dimensional tests for spherical location and spiked covariance," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 79-91.
    3. Christine Cutting & Davy Paindaveine & Thomas Verdebout, 2015. "Testing Uniformity on High-Dimensional Spheres against Contiguous Rotationally Symmetric Alternatives," Working Papers ECARES ECARES 2015-04, ULB -- Universite Libre de Bruxelles.
    4. P. V. Larsen, 2002. "Improved likelihood ratio tests on the von Mises--Fisher distribution," Biometrika, Biometrika Trust, vol. 89(4), pages 947-951, December.
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