Combining L1 and L2 Norms for a more Robust Spatial Analysis: the "Meadian Attitude"

• Main Authors: Didier Josselin, Dominique Ladiray
• Format: Article
• Language: deu
• Published: Unité Mixte de Recherche 8504 Géographie-cités 2002-08-01
• Series: Cybergeo
• Subjects: meadian; robustness; mean; median; L-estimators; bootstrap
• Online Access: http://journals.openedition.org/cybergeo/3458

This paper presents a new way to look for the "center" of a statistical distribution. This concept basically combines the mean and the median, i.e. two L-norms, to define a new metric in order to improve the robustness of efficiency of an estimator. After a short historical presentation of the relationships between the mean and the median in the quest for the "center", we explain the problematic that leads us to propose a new estimator. We define the meadian, a first version of which was set up by Laplace in the early 1800s, and present its asymptotic properties. We justify the choice of bootstrap to compute the variances involved in the meadians definition. Some applications in spatial filtering are presented and discussed. In conclusion, we comment on some further developments and perspectives for the "meadian attitude".