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 \(p > 2\).
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Acknowledgements
The research of the first two authors is supported by National Natural Science Foundation of China (Grant No.11601197, 11461029, 61563018), Ministry of Education Humanity Social Science Research Project of China (No.15JYC910002), China Postdoctoral Science Foundation funded project (2016M600511, 2017T100475), NSF of Jiangxi Province (No.20171ACB21030, 20161BAB201024, 20161ACB20009), and the Key Science Fund Project of Jiangxi provincial education department (No.GJJ150439, KJLD13033, KJLD14034). We thank the Editor-in-Chief Professor Müller, C., the AE, two anonymous reviewers and Yuanyuan Li for their careful reading and insightful comments, which led to many improvements in this paper.
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Liu, X., Luo, S. & Zuo, Y. Some results on the computing of Tukey’s halfspace median. Stat Papers 61, 303–316 (2020). https://doi.org/10.1007/s00362-017-0941-5
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DOI: https://doi.org/10.1007/s00362-017-0941-5