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An integrated local depth measure

Author

Listed:
  • Lucas Fernandez-Piana

    (Universidad de San Andrés)

  • Marcela Svarc

    (Universidad de San Andrés
    CONICET)

Abstract

We introduce the Integrated Dual Local Depth, which is a local depth measure for data in a Banach space based on the use of one-dimensional projections. The properties of a depth measure are analyzed under this setting and a proper definition of local symmetry is given. Moreover, strong consistency results for the local depth and also, for local depth regions are attained. Finally, applications to descriptive data analysis and classification are analyzed, making a special focus on multivariate functional data, where we obtain very promising results.

Suggested Citation

  • Lucas Fernandez-Piana & Marcela Svarc, 2022. "An integrated local depth measure," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(2), pages 175-197, June.
    • Handle: RePEc:spr:alstar:v:106:y:2022:i:2:d:10.1007_s10182-021-00424-6
    DOI: 10.1007/s10182-021-00424-6
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    References listed on IDEAS

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    1. Carlo Sguera & Pedro Galeano & Rosa Lillo, 2014. "Spatial depth-based classification for functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(4), pages 725-750, December.
    2. Kotík, Lukáš & Hlubinka, Daniel, 2017. "A weighted localization of halfspace depth and its properties," Journal of Multivariate Analysis, Elsevier, vol. 157(C), pages 53-69.
    3. Davy Paindaveine & Germain Van bever, 2013. "From Depth to Local Depth: A Focus on Centrality," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(503), pages 1105-1119, September.
    4. Cuevas, Antonio & Fraiman, Ricardo, 2009. "On depth measures and dual statistics. A methodology for dealing with general data," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 753-766, April.
    5. Agostinelli, Claudio, 2018. "Local half-region depth for functional data," Journal of Multivariate Analysis, Elsevier, vol. 163(C), pages 67-79.
    6. Antonio Cuevas & Manuel Febrero & Ricardo Fraiman, 2007. "Robust estimation and classification for functional data via projection-based depth notions," Computational Statistics, Springer, vol. 22(3), pages 481-496, September.
    7. Cuesta-Albertos, J.A. & Nieto-Reyes, A., 2008. "The random Tukey depth," Computational Statistics & Data Analysis, Elsevier, vol. 52(11), pages 4979-4988, July.
    8. Nieto-Reyes, Alicia & Battey, Heather, 2021. "A topologically valid construction of depth for functional data," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
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    Full references (including those not matched with items on IDEAS)

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