Some results on the computing of Tukey’s halfspace median

Xiaohui Liu (), Shihua Luo and Yijun Zuo
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Xiaohui Liu: Jiangxi University of Finance and Economics
Shihua Luo: Jiangxi University of Finance and Economics
Yijun Zuo: Michigan State University

Statistical Papers, 2020, vol. 61, issue 1, No 16, 303-316

Abstract: Abstract Depth of the Tukey median is investigated for empirical distributions. A sharper upper bound is provided for this value for data sets in general position. This bound is lower than the existing one in the literature and, more importantly, derived under the fixed sample size practical scenario. Several results obtained in this paper are interesting theoretically and useful as well to reduce the computational burden of the Tukey median practically when $$p > 2$$p>2.

Keywords: Data depth; Tukey median; Maximum halfspace depth; General position; 62F10; 62F40; 62F35 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s00362-017-0941-5

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