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Lundi 22 mai 2017

Intervenant : Pavlo MOZHAROWSKYI (CREST, ENSAI, Université Bretagne Loire)

« Statistical depth function and its application in classification » 

De 15h à 16h15, en salle 08 à l'ENSAE : 3, avenue Pierre Larousse à Malakoff (Tram T3 : arrêt « Porte de Vanves » ou Métro - ligne 13 station  : « Porte de Vanves » ou « Malakoff Plateau de Vanves »)

Following the seminal idea of John W. Tukey, data depth is a function that measures how close an arbitrary point of the space is located to an implicitly defined center of a data cloud. Having undergone theoretical and computational developments, it is now employed in numerous applications with classification being the most popular one. This presentation suggests an overview of some key results in the area of the depth function. First, a general introduction to the concept of data depth in an Euclidean space and to the multivariate trimming it implies is given. Next, properties of the most employed depth notions are analyzed: Mahalanobis, spatial, projection, zonoid, and halfspace depth; this last one deserves a special attention due to numerous (recent) developments. Further, special classes of the depth function are considered such as depths satisfying the projection property or depths induced by a weighted-mean trimming. The question of convergence of the depth process is addressed as well. After this, localization of depths is regarded, which permits to account for multimodality of the underlying distribution. This and further properties of the depth function allow to construct depth-based classifiers such as the maximum depth classifier, the $DD$-plot classifier, the depth-$k$NN, and the multi-scale spatial-depth-classifier. Finally, extension of the data depth to a functional framework is introduced.

Ce séminaire est organisé par :

Alexandre TSYBAKOV         (Laboratoire de Statistique-CREST)

Cristina BUTUCEA                (Laboratoire de Statistique-CREST)