General notions of depth for functional data

Karl Mosler; Yulia Polyakova

General notions of depth for functional data

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arxiv 1208.1981 v3 pith:6FXVWLJT submitted 2012-08-09 stat.ME

Karl Mosler , Yulia Polyakova This is my paper

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keywords depthdatageneralapproachdepthsfunctionalnotionsphi-depth

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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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Locally Adaptive Conformal Inference for Operator Models
stat.ML 2025-07 conditional novelty 6.0 of 10

LSCI constructs function-valued, locally adaptive conformal prediction sets for operator models by weighting a functional depth score around the test input, with a coverage-gap bound under local exchangeability.

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