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

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...

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Autores principales:	Didier Josselin, Dominique Ladiray
Formato:	article
Lenguaje:	DE EN FR IT PT
Publicado:	Unité Mixte de Recherche 8504 Géographie-cités 2002
Materias:	meadian robustness mean median L-estimators bootstrap Geography (General) G1-922
Acceso en línea:	https://doaj.org/article/c7ce5e0afcf04d98a113b80710f7fcf6
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id	oai:doaj.org-article:c7ce5e0afcf04d98a113b80710f7fcf6
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spelling	oai:doaj.org-article:c7ce5e0afcf04d98a113b80710f7fcf62021-12-02T11:19:43ZCombining L1 and L2 Norms for a more Robust Spatial Analysis: the "Meadian Attitude"1278-336610.4000/cybergeo.3458https://doaj.org/article/c7ce5e0afcf04d98a113b80710f7fcf62002-08-01T00:00:00Zhttp://journals.openedition.org/cybergeo/3458https://doaj.org/toc/1278-3366This 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".Didier JosselinDominique LadirayUnité Mixte de Recherche 8504 Géographie-citésarticlemeadianrobustnessmeanmedianL-estimatorsbootstrapGeography (General)G1-922DEENFRITPTCybergeo (2002)
institution	DOAJ
collection	DOAJ
language	DE EN FR IT PT
topic	meadian robustness mean median L-estimators bootstrap Geography (General) G1-922
spellingShingle	meadian robustness mean median L-estimators bootstrap Geography (General) G1-922 Didier Josselin Dominique Ladiray Combining L1 and L2 Norms for a more Robust Spatial Analysis: the "Meadian Attitude"
description	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".
format	article
author	Didier Josselin Dominique Ladiray
author_facet	Didier Josselin Dominique Ladiray
author_sort	Didier Josselin
title	Combining L1 and L2 Norms for a more Robust Spatial Analysis: the "Meadian Attitude"
title_short	Combining L1 and L2 Norms for a more Robust Spatial Analysis: the "Meadian Attitude"
title_full	Combining L1 and L2 Norms for a more Robust Spatial Analysis: the "Meadian Attitude"
title_fullStr	Combining L1 and L2 Norms for a more Robust Spatial Analysis: the "Meadian Attitude"
title_full_unstemmed	Combining L1 and L2 Norms for a more Robust Spatial Analysis: the "Meadian Attitude"
title_sort	combining l1 and l2 norms for a more robust spatial analysis: the "meadian attitude"
publisher	Unité Mixte de Recherche 8504 Géographie-cités
publishDate	2002
url	https://doaj.org/article/c7ce5e0afcf04d98a113b80710f7fcf6
work_keys_str_mv	AT didierjosselin combiningl1andl2normsforamorerobustspatialanalysisthemeadianattitude AT dominiqueladiray combiningl1andl2normsforamorerobustspatialanalysisthemeadianattitude
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Combining L1 and L2 Norms for a more Robust Spatial Analysis: the "Meadian Attitude"

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