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Generalized and robustified empirical depths for multivariate data

Author

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  • Liu, Xiaohui
  • Rahman, Jafer
  • Luo, Shihua

Abstract

In this paper, we point out a common feature of zonoid and empirical depths that gives rise to a novel class of data depths, and provide a possible robustification of their deepest points. This general approach may be useful as it allows the robustification of the zonoid depth and other depths that are centered at the usual mean. Illustrations are also provided to demonstrate the depth contours induced from these depths based on a real data set.

Suggested Citation

  • Liu, Xiaohui & Rahman, Jafer & Luo, Shihua, 2019. "Generalized and robustified empirical depths for multivariate data," Statistics & Probability Letters, Elsevier, vol. 146(C), pages 70-79.
    • Handle: RePEc:eee:stapro:v:146:y:2019:i:c:p:70-79
    DOI: 10.1016/j.spl.2018.10.018
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    References listed on IDEAS

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    1. Liu, Xiaohui & Zuo, Yijun, 2015. "CompPD: A MATLAB Package for Computing Projection Depth," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 65(i02).
    2. 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.
    3. Tsao, Min, 2013. "An empirical depth function for multivariate data," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 213-218.
    4. Tatjana Lange & Karl Mosler & Pavlo Mozharovskyi, 2014. "Fast nonparametric classification based on data depth," Statistical Papers, Springer, vol. 55(1), pages 49-69, February.
    5. Ignacio Cascos & Ilya Molchanov, 2007. "Multivariate risks and depth-trimmed regions," Finance and Stochastics, Springer, vol. 11(3), pages 373-397, July.
    6. Dyckerhoff, Rainer & Mosler, Karl, 2011. "Weighted-mean trimming of multivariate data," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 405-421, March.
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