La médiane simpliciale d'Oja: Existence,unicité et stabilité

Oja (1983) examined various ways of measuring location, scatter, skewness, and kurtosis for multivariate distributions. Among other measures of location, he introduced a generalised median known in this paper under the name of the Oja median. In our study of the existence of that median, we show that Oja's definition can only be applied to distributions having a mean. In dimension d θ 2, we establish that the usual method of extension breaks down, which raises the question of the validity of the concept as a notion of median. Two fundamental theoretical properties of that median are also considered: uniqueness and consistency.