Chan, Y. M.; He, Xuming On median-type estimators of direction for the von Mises-Fisher distribution. (English) Zbl 0795.62053 Biometrika 80, No. 4, 869-875 (1993). 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. Cited in 7 Documents MSC: 62H11 Directional data; spatial statistics 62H12 Estimation in multivariate analysis 62F12 Asymptotic properties of parametric estimators Keywords:directional data; gross-error sensitivity; von Mises-Fisher distribution; L1-estimators; median-type estimators; normalized spatial median; spherical median; efficiencies; influence functions; sensitivities; simulation study; finite sample performance; mean squared errors Software:ESTIMA PDFBibTeX XMLCite \textit{Y. M. Chan} and \textit{X. He}, Biometrika 80, No. 4, 869--875 (1993; Zbl 0795.62053)