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

Luis González- De La Fuente, Alicia Nieto-Reyes and Pedro Terán
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Luis González- De La Fuente: Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, 39005 Santander, Spain
Alicia Nieto-Reyes: Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, 39005 Santander, Spain
Pedro Terán: Departamento de Estadística e Investigación Operativa y Didáctica de las Matemáticas, Universidad de Oviedo, 33007 Oviedo, Spain

Mathematics, 2022, vol. 10, issue 15, 1-23

Abstract: 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.

Keywords: compact convex set; halfspace depth; statistical depth function; symmetry (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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