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The Tukey Depth Characterizes the Atomic Measure

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  • Koshevoy, Gleb A.

Abstract

We prove that if the Tukey depths of two atomic measures are identical, then the measures are also identical.

Suggested Citation

  • Koshevoy, Gleb A., 2002. "The Tukey Depth Characterizes the Atomic Measure," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 360-364, November.
  • Handle: RePEc:eee:jmvana:v:83:y:2002:i:2:p:360-364
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    References listed on IDEAS

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    1. Nolan, D., 1992. "Asymptotics for multivariate trimming," Stochastic Processes and their Applications, Elsevier, vol. 42(1), pages 157-169, August.
    2. 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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    Cited by:

    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. 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. Kong, Linglong & Zuo, Yijun, 2010. "Smooth depth contours characterize the underlying distribution," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2222-2226, October.
    4. Xiaohui Liu & Karl Mosler & Pavlo Mozharovskyi, 2017. "Fast computation of Tukey trimmed regions and median in dimension p > 2," Working Papers 2017-71, Center for Research in Economics and Statistics.
    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. Dyckerhoff, Rainer & Mozharovskyi, Pavlo, 2016. "Exact computation of the halfspace depth," Computational Statistics & Data Analysis, Elsevier, vol. 98(C), pages 19-30.
    7. Cuesta-Albertos, J.A. & Nieto-Reyes, A., 2008. "The Tukey and the random Tukey depths characterize discrete distributions," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2304-2311, November.

    More about this item

    Keywords

    halfspace depth depth contour;

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