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General notions of depth for functional data

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 نشر من قبل Karl Mosler
 تاريخ النشر 2012
  مجال البحث الاحصاء الرياضي
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A data depth measures the centrality of a point with respect to an empirical distribution. Postulates are formulated, which a depth for functional data should satisfy, and a general approach is proposed to construct multivariate data depths in Banach spaces. The new approach, mentioned as Phi-depth, is based on depth infima over a proper set Phi of R^d-valued linear functions. Several desirable properties are established for the Phi-depth and a generalized version of it. The general notions include many new depths as special cases. In particular a location-slope depth and a principal component depth are introduced.



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