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, L 1 -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.