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Bahadur representations for the bootstrap median absolute deviation and the application to projection depth weighted mean

Author

Listed:
  • Qing Liu

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

  • Xiaohui Liu

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

  • Zihao Hu

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

Abstract

Median absolute deviation (hereafter MAD) is known as a robust alternative to the ordinary variance. It has been widely utilized to induce robust statistical inferential procedures. In this paper, we investigate the strong and weak Bahadur representations of its bootstrap counterpart. As a useful application, we utilize the results to derive the weak Bahadur representation of the bootstrap sample projection depth weighted mean—a quite important location estimator depending on MAD.

Suggested Citation

  • Qing Liu & Xiaohui Liu & Zihao Hu, 2025. "Bahadur representations for the bootstrap median absolute deviation and the application to projection depth weighted mean," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 88(3), pages 341-364, April.
    • Handle: RePEc:spr:metrik:v:88:y:2025:i:3:d:10.1007_s00184-024-00958-0
    DOI: 10.1007/s00184-024-00958-0
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    References listed on IDEAS

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    1. Serfling, Robert & Mazumder, Satyaki, 2009. "Exponential probability inequality and convergence results for the median absolute deviation and its modifications," Statistics & Probability Letters, Elsevier, vol. 79(16), pages 1767-1773, August.
    2. Michael Falk, 1997. "On Mad and Comedians," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(4), pages 615-644, December.
    3. Mazumder, Satyaki & Serfling, Robert, 2009. "Bahadur representations for the median absolute deviation and its modifications," Statistics & Probability Letters, Elsevier, vol. 79(16), pages 1774-1783, August.
    4. Yijun Zuo, 2015. "Bahadur representations for bootstrap quantiles," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(5), pages 597-610, July.
    5. Subhajit Dutta & Anil Ghosh, 2012. "On robust classification using projection depth," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(3), pages 657-676, June.
    6. Wendler, Martin, 2011. "Bahadur representation for U-quantiles of dependent data," Journal of Multivariate Analysis, Elsevier, vol. 102(6), pages 1064-1079, July.
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