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

Author

Listed:
  • 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
    Current address: Facultad de Ciencias, Avd. de los Castros s/n, 39005 Santander, Spain.)

  • Pedro Terán

    (Departamento de Estadística e Investigación Operativa y Didáctica de las Matemáticas, Universidad de Oviedo, 33007 Oviedo, Spain)

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.

Suggested Citation

  • Luis González-De La Fuente & Alicia Nieto-Reyes & Pedro Terán, 2022. "Properties of Statistical Depth with Respect to Compact Convex Random Sets: The Tukey Depth," Mathematics, MDPI, vol. 10(15), pages 1-23, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2758-:d:879481
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    References listed on IDEAS

    as
    1. Alicia Nieto-Reyes & Heather Battey & Giacomo Francisci, 2021. "Functional Symmetry and Statistical Depth for the Analysis of Movement Patterns in Alzheimer’s Patients," Mathematics, MDPI, vol. 9(8), pages 1-17, April.
    2. SALINETTI, Gabriella & WETS, Roger J.-B., 1979. "On the convergence of sequences of convex sets in finite dimensions," LIDAM Reprints CORE 352, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Cuesta-Albertos, J.A. & Nieto-Reyes, A., 2008. "The random Tukey depth," Computational Statistics & Data Analysis, Elsevier, vol. 52(11), pages 4979-4988, July.
    4. Nieto-Reyes, Alicia & Battey, Heather, 2021. "A topologically valid construction of depth for functional data," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    5. Alicia Nieto-Reyes & Rafael Duque & Giacomo Francisci, 2021. "A Method to Automate the Prediction of Student Academic Performance from Early Stages of the Course," Mathematics, MDPI, vol. 9(21), pages 1-14, October.
    6. Dias, Sónia & Brito, Paula, 2017. "Off the beaten track: A new linear model for interval data," European Journal of Operational Research, Elsevier, vol. 258(3), pages 1118-1130.
    Full references (including those not matched with items on IDEAS)

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