Finite Sample ``Tail'' Behavior of Multivariate Location Estimators

Keywords: Tail behavior, location estimator, breakdown point, monotone estimator, halfspace median, L-statistics, Hodges-Lehmann estimator

Abstract: A finite sample performance measure of multivariate location estimators is introduced based on ``tail'' behavior. The performance of various location estimators, inculding multivariate monotone location estimators, multivariate robust location estimators, Tukey-Donoho halfspace median, Hodges-Lehmann type estimators, with respect to this measure is investigated. The interconnections of our finite sample performance measure with the notion of finite sample breakdown point and the notion of halfspace depth are explored.