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Trimmed and winsorized standard deviations based on a scaled deviation

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  • Mingxin Wu
  • Yijun Zuo

Abstract

Trimmed (and winsorized) standard deviations based on a scaled deviation are introduced and studied. The influence functions and limiting distributions are obtained. The performance of the estimators with respect to high breakdown scale estimators is evaluated and compared. Unlike other high breakdown estimators which perform poorly for light-tailed distribution and when points near the centre are contaminated, the resulting trimmed (and winsorized) standard deviations are much more efficient than their predecessors at light-tailed distributions by suitably choosing the cutting parameter and highly efficient for heavy-tailed and skewed distributions. At the same time, they share the best breakdown point robustness of the sample median absolute deviation for any common trimming thresholds. Compared with their predecessors, they can achieve the best efficiency when the contaminating points are presented from areas around the centre. Indeed, the scaled-deviation-trimmed (winsorized) standard deviations behave very well overall and, consequently, represent very favourable alternatives to existing scale estimators.

Suggested Citation

  • Mingxin Wu & Yijun Zuo, 2008. "Trimmed and winsorized standard deviations based on a scaled deviation," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(4), pages 319-335.
    • Handle: RePEc:taf:gnstxx:v:20:y:2008:i:4:p:319-335
    DOI: 10.1080/10485250802036909
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    References listed on IDEAS

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    1. Jana Jurečková & Roger Koenker & A. Welsh, 1994. "Adaptive choice of trimming proportions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(4), pages 737-755, December.
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    Cited by:

    1. Indranil Ghosh & Kathleen Fleming, 2022. "On the Robustness and Sensitivity of Several Nonparametric Estimators via the Influence Curve Measure: A Brief Study," Mathematics, MDPI, vol. 10(17), pages 1-16, August.
    2. Yijun Zuo, 2020. "Depth Induced Regression Medians and Uniqueness," Stats, MDPI, vol. 3(2), pages 1-13, April.
    3. Zuo, Yijun, 2021. "Computation of projection regression depth and its induced median," Computational Statistics & Data Analysis, Elsevier, vol. 158(C).
    4. Yijun Zuo, 2021. "Robustness of the deepest projection regression functional," Statistical Papers, Springer, vol. 62(3), pages 1167-1193, June.

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    1. Dodge, Yadolah & Jurecková, Jana, 1997. "Adaptive choice of trimming proportion in trimmed least-squares estimation," Statistics & Probability Letters, Elsevier, vol. 33(2), pages 167-176, April.

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