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Halfspace depth does not characterize probability distributions

Author

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  • Stanislav Nagy

    (Charles University)

Abstract

We give examples of different multivariate probability distributions whose halfspace depths coincide at all points of the sample space.

Suggested Citation

  • Stanislav Nagy, 2021. "Halfspace depth does not characterize probability distributions," Statistical Papers, Springer, vol. 62(3), pages 1135-1139, June.
    • Handle: RePEc:spr:stpapr:v:62:y:2021:i:3:d:10.1007_s00362-019-01130-x
    DOI: 10.1007/s00362-019-01130-x
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    References listed on IDEAS

    as
    1. Hassairi, Abdelhamid & Regaieg, Ons, 2008. "On the Tukey depth of a continuous probability distribution," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2308-2313, October.
    2. Einmahl, J.H.J. & Li, Jun & Liu, Regina, 2015. "Bridging Centrality and Extremity : Refining Empirical Data Depth using Extreme Value Statistics," Other publications TiSEM bcd9783a-e07e-4da2-bc47-b, Tilburg University, School of Economics and Management.
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    5. Struyf, Anja J. & Rousseeuw, Peter J., 1999. "Halfspace Depth and Regression Depth Characterize the Empirical Distribution," Journal of Multivariate Analysis, Elsevier, vol. 69(1), pages 135-153, April.
    6. Mengta Yang & Reza Modarres, 2017. "Multivariate tests of uniformity," Statistical Papers, Springer, vol. 58(3), pages 627-639, September.
    7. Kong, Linglong & Zuo, Yijun, 2010. "Smooth depth contours characterize the underlying distribution," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2222-2226, October.
    8. Tatjana Lange & Karl Mosler & Pavlo Mozharovskyi, 2014. "Fast nonparametric classification based on data depth," Statistical Papers, Springer, vol. 55(1), pages 49-69, February.
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    Full references (including those not matched with items on IDEAS)

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