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On the Tukey depth of a continuous probability distribution

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  • Hassairi, Abdelhamid
  • Regaieg, Ons

Abstract

In this paper, we prove that, under some regularity condition, the Tukey depth function of an absolutely continuous probability distribution characterizes the distribution.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:15:p:2308-2313
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    References listed on IDEAS

    as
    1. Masse, J. C. & Theodorescu, R., 1994. "Halfplane Trimming for Bivariate Distributions," Journal of Multivariate Analysis, Elsevier, vol. 48(2), pages 188-202, February.
    2. Koshevoy, Gleb A., 2002. "The Tukey Depth Characterizes the Atomic Measure," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 360-364, November.
    3. 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.
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    Citations

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    Cited by:

    1. Stanislav Nagy, 2021. "Halfspace depth does not characterize probability distributions," Statistical Papers, Springer, vol. 62(3), pages 1135-1139, June.
    2. Victor Chernozhukov & Alfred Galichon & Marc Hallin & Marc Henry, 2014. "Monge-Kantorovich Depth, Quantiles, Ranks, and Signs," Papers 1412.8434, arXiv.org, revised Sep 2015.
    3. repec:spo:wpmain:info:hdl:2441/64itsev5509q8aa5mrbhi0g0b6 is not listed on IDEAS
    4. Victor Chernozhukov & Alfred Galichon & Marc Hallin & Marc Henry, 2014. "Monge-Kantorovich Depth, Quantiles, Ranks, and Signs," Papers 1412.8434, arXiv.org, revised Sep 2015.
    5. Wei, Bei & Lee, Stephen M.S., 2012. "Second-order accuracy of depth-based bootstrap confidence regions," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 112-123.
    6. repec:hal:spmain:info:hdl:2441/64itsev5509q8aa5mrbhi0g0b6 is not listed on IDEAS
    7. repec:hal:spmain:info:hdl:2441/3qnaslliat80pbqa8t90240unj is not listed on IDEAS
    8. Laketa, Petra & Nagy, Stanislav, 2021. "Reconstruction of atomic measures from their halfspace depth," Journal of Multivariate Analysis, Elsevier, vol. 183(C).

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