On median-type estimators of direction for the von mises-fisher distribution

Abstract

SUMMARY: 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. © 1993 Biometrika Trust.