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Biometrika 1993 80(4):869-875; doi:10.1093/biomet/80.4.869
© 1993 by Biometrika Trust
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On median-type estimators of direction for the von Mises—Fisher distribution

Y. M. CHAN and XUMING HE

Department of Mathematics, National University of Singapore Singapore 0511
Department of Statistics, University of Illinois, Champaign Illinois 61820, U.S.A.

We study three median-type estimators of direction: the normalized spatial median, L1-estimator on the sphere and spherical median. Their asymptotic distributions, efficiencies, influence functions and sensitivities are given at the von Mises-Fisher model. A simulation study is also carried out to compare their finite sample performance in terms of mean squared errors. We conclude that overall the normalized spatial median is the preferred estimator.

Key Words: Asymptotic distribution • Directional data • Efficiency • Gross-error sensitivity • Influence function • L1-estimator • Spatial median • Spherical median • von Mises-Fisher distribution


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