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Multidimensional medians and uniqueness

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  • Zuo, Yijun

Abstract

Multidimensional medians induced from depth functions as the generalizations of the univariate median have been proposed and studied. Like their univariate counterpart, they usually possess the desirable properties including affine equivariance, high breakdown point robustness, etc. Furthermore, they could serve as the deepest point (a location measure) of the underlying distribution. The most prominent and prevail depth median is Tukey’s halfspace median. However, like most of other depth medians, it is generally not unique. On the other hand, we show that the projection median distinguishes itself from its competitors and possesses the desirable uniqueness property.

Suggested Citation

  • Zuo, Yijun, 2013. "Multidimensional medians and uniqueness," Computational Statistics & Data Analysis, Elsevier, vol. 66(C), pages 82-88.
    • Handle: RePEc:eee:csdana:v:66:y:2013:i:c:p:82-88
    DOI: 10.1016/j.csda.2013.03.020
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    References listed on IDEAS

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    1. Liu, Xiaohui & Zuo, Yijun & Wang, Zhizhong, 2013. "Exactly computing bivariate projection depth contours and median," Computational Statistics & Data Analysis, Elsevier, vol. 60(C), pages 1-11.
    2. Marc Hallin & Davy Paindaveine & Miroslav Siman, 2008. "Multivariate quantiles and multiple-output regression quantiles: from L1 optimization to halfspace depth," Working Papers ECARES 2008_042, ULB -- Universite Libre de Bruxelles.
    3. Oja, Hannu, 1983. "Descriptive statistics for multivariate distributions," Statistics & Probability Letters, Elsevier, vol. 1(6), pages 327-332, October.
    4. Zuo, Yijun & Lai, Shaoyong, 2011. "Exact computation of bivariate projection depth and the Stahel-Donoho estimator," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1173-1179, March.
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    Cited by:

    1. Aubin, Jean-Baptiste & Gannaz, Irène & Leoni, Samuela & Rolland, Antoine, 2022. "Deepest voting: A new way of electing," Mathematical Social Sciences, Elsevier, vol. 116(C), pages 1-16.
    2. Yijun Zuo, 2020. "Depth Induced Regression Medians and Uniqueness," Stats, MDPI, vol. 3(2), pages 1-13, April.
    3. Sinova, Beatriz & Van Aelst, Stefan, 2015. "On the consistency of a spatial-type interval-valued median for random intervals," Statistics & Probability Letters, Elsevier, vol. 100(C), pages 130-136.

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