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

Qing Liu, Xiaohui Liu () and Zihao Hu
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Qing Liu: Jiangxi University of Finance and Economics
Xiaohui Liu: Jiangxi University of Finance and Economics
Zihao Hu: Jiangxi University of Finance and Economics

Metrika: International Journal for Theoretical and Applied Statistics, 2025, vol. 88, issue 3, No 3, 364 pages

Abstract: 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.

Keywords: Bootstrap MAD; Bootstrap projection depth weighted mean; Bahadur representation; 62F10; 62F40; 62F35 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00184-024-00958-0

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