Tukey Depth for Fuzzy Sets

Fuente, Luis González-De La; Nieto-Reyes, Alicia; Terán, Pedro

doi:10.1007/978-3-031-15509-3_25

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2022

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“…It is worth noting that the spatial and random Tukey depth functions were introduced before the functional axiomatic definition in [16]. Furthermore, while the Tukey depth has not yet being defined in functional spaces, it has being generalized to the fuzzy setting and proved to satisfy the axiomatic definitions in that setting [15,23].…”

Section: Introductionmentioning

confidence: 99%

Properties of Statistical Depth with Respect to Compact Convex Random Sets: The Tukey Depth

2022

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We study a statistical data depth with respect to compact convex random sets, which is consistent with the multivariate Tukey depth and the Tukey depth for fuzzy sets. In addition, it provides a different perspective to the existing halfspace depth with respect to compact convex random sets. In studying this depth function, we provide a series of properties for the statistical data depth with respect to compact convex random sets. These properties are an adaptation of properties that constitute the axiomatic notions of multivariate, functional, and fuzzy depth-functions and other well-known properties of depth.

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Section: Introductionmentioning

confidence: 99%