General notions of depth for functional data

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,...

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Bibliographic Details
Published in:arXiv.org 2018-01
Main Authors: Mosler, Karl, Polyakova, Yulia
Format: Article
Language:English
Subjects:
Banach spaces
Economic models
Linear functions
Multivariate analysis
Online Access:Get full text
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Summary: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.
ISSN:2331-8422