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Biometrika 1987 74(1):212-215; doi:10.1093/biomet/74.1.212
© 1987 by Biometrika Trust
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MISCELLANEA

Spatial median and directional data

GILLES R. DUCHARME and PHILIP MILASEVIC

Département de mathématiques et de statistique, Université de Montréal Montréal, P.Q. H3C 3J7
Institut de mathématiques, Université de Fribourg 1700 Fribourg, Switzerland

We introduce the normalized spatial median as an estimator of location for rotationally symmetric distributions on the hypersphere. We investigate some of its asymptotic properties and use them to obtain confidence regions for the modal direction of a distribution on the hypersphere. These results are then applied to the von Mises-Fisher distribution and to a contamination model. It is seen that the normalized spatial median can perform more efficiently than the normalized mean in presence of outliers.

Key Words: Asymptotic relative efficiency • Directional data • Outlier • Rotational symmetry • Spatial median • von Mises-Fisher distribution


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