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Some results on the computing of Tukey’s halfspace median

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  • Xiaohui Liu

    (Jiangxi University of Finance and Economics
    Jiangxi University of Finance and Economics)

  • Shihua Luo

    (Jiangxi University of Finance and Economics
    Jiangxi University of Finance and Economics)

  • Yijun Zuo

    (Michigan State University)

Abstract

Depth of the Tukey median is investigated for empirical distributions. A sharper upper bound is provided for this value for data sets in general position. This bound is lower than the existing one in the literature and, more importantly, derived under the fixed sample size practical scenario. Several results obtained in this paper are interesting theoretically and useful as well to reduce the computational burden of the Tukey median practically when $$p > 2$$p>2.

Suggested Citation

  • Xiaohui Liu & Shihua Luo & Yijun Zuo, 2020. "Some results on the computing of Tukey’s halfspace median," Statistical Papers, Springer, vol. 61(1), pages 303-316, February.
    • Handle: RePEc:spr:stpapr:v:61:y:2020:i:1:d:10.1007_s00362-017-0941-5
    DOI: 10.1007/s00362-017-0941-5
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    References listed on IDEAS

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    1. Paindaveine, Davy & Siman, Miroslav, 2011. "On directional multiple-output quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 102(2), pages 193-212, February.
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    3. Struyf, Anja & Rousseeuw, Peter J., 2000. "High-dimensional computation of the deepest location," Computational Statistics & Data Analysis, Elsevier, vol. 34(4), pages 415-426, October.
    4. Ruts, Ida & Rousseeuw, Peter J., 1996. "Computing depth contours of bivariate point clouds," Computational Statistics & Data Analysis, Elsevier, vol. 23(1), pages 153-168, November.
    5. Dyckerhoff, Rainer & Mozharovskyi, Pavlo, 2016. "Exact computation of the halfspace depth," Computational Statistics & Data Analysis, Elsevier, vol. 98(C), pages 19-30.
    6. Mosler, Karl & Lange, Tatjana & Bazovkin, Pavel, 2009. "Computing zonoid trimmed regions of dimension d>2," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2500-2510, May.
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