General notions of depth for functional data

Karl Mosler; Yulia Polyakova

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arXiv · 1208.1981

General notions of depth for functional data

Karl Mosler·Yulia Polyakova

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Abstract

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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Karl Mosler, Yulia Polyakova. 2012-08-09. General notions of depth for functional data. https://arxiv.org/abs/1208.1981

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