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Tests for the mean direction of the Langevin distribution with large concentration parameter

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  • Fujikoshi, Yasunori
  • Watamori, Yoko

Abstract

In this paper we study the asymptotic behaviors of the likelihood ratio criterion (TL(s)), Watson statistic (TW(s)) and Rao statistic (TR(s)) for testing H0s: [mu] [set membership, variant] (a given subspace) against H1s: [mu] [negated set membership] , based on a sample of size n from a p-variate Langevin distribution Mp([mu], ?) when ? is large. For the case when ? is known, asymptotic expansions of the null and nonnull distributions of these statistics are obtained. It is shown that the powers of these statistics are coincident up to the order ?-1. For the case when ? is unknown, it is shown that TR(s) [greater, double equals] TL(s) [greater, double equals] TW(s) in their powers up to the order ?-1.

Suggested Citation

  • Fujikoshi, Yasunori & Watamori, Yoko, 1992. "Tests for the mean direction of the Langevin distribution with large concentration parameter," Journal of Multivariate Analysis, Elsevier, vol. 42(2), pages 210-225, August.
  • Handle: RePEc:eee:jmvana:v:42:y:1992:i:2:p:210-225
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    Cited by:

    1. Davy Paindaveine & Thomas Verdebout, 2019. "Inference for Spherical Location under High Concentration," Working Papers ECARES 2019-02, ULB -- Universite Libre de Bruxelles.

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