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La médiane simpliciale d'Oja: Existence, unicité et stabilité
Author(s) -
LeÓan Carlos Antonio,
Massé JeanClaude
Publication year - 1993
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315703
Subject(s) - kurtosis , skewness , mathematics , consistency (knowledge bases) , dimension (graph theory) , uniqueness , multivariate statistics , statistics , extension (predicate logic) , econometrics , mathematical analysis , pure mathematics , discrete mathematics , computer science , programming language
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.