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The admissibility of the empirical mean location for the matrix von Mises-Fisher family

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  • Hendriks, Harrie

Abstract

In this note we consider von Mises-Fisher families of probability densities on spheres and more generally on Stiefel manifolds, which include the orthogonal groups. It addresses the estimation of the mean direction or the mean location by empirical mean location, which for the von Mises-Fisher family coincides with the maximum likelihood estimator. It is shown that (with a few exceptions) the empirical mean location of a sample is almost surely uniquely defined and that it is unbiased in the sense that its mean location coincides with the mean location of the von Mises-Fisher distribution. The main goal, however, is to show that empirical mean location is an admissible estimator for the mean location of the von Mises-Fisher distribution.

Suggested Citation

  • Hendriks, Harrie, 2005. "The admissibility of the empirical mean location for the matrix von Mises-Fisher family," Journal of Multivariate Analysis, Elsevier, vol. 92(2), pages 454-464, February.
  • Handle: RePEc:eee:jmvana:v:92:y:2005:i:2:p:454-464
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    References listed on IDEAS

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    1. Hendriks, Harrie, 1991. "A Cramér-Rao type lower bound for estimators with values in a manifold," Journal of Multivariate Analysis, Elsevier, vol. 38(2), pages 245-261, August.
    2. Kim, Peter T., 1991. "Decision theoretic analysis of spherical regression," Journal of Multivariate Analysis, Elsevier, vol. 38(2), pages 233-240, August.
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    Cited by:

    1. Kanika, & Kumar, Somesh & SenGupta, Ashis, 2015. "A unified approach to decision-theoretic properties of the MLEs for the mean directions of several Langevin distributions," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 160-172.

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