Finite sample breakdown point of Tukey's halfspace median

doi:10.1007/s11425-016-0285-1

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	Finite sample breakdown point of Tukey's halfspace median
	Liu, XiaoHui 1,2; Zuo, YiJun 3; Wang, QiHua4,5
刊名	SCIENCE CHINA-MATHEMATICS
	2017-05-01
卷号	60 期号:5 页码:861-874
关键词	Tukey depth Tukey median breakdown point in general position
ISSN号	1674-7283
DOI	10.1007/s11425-016-0285-1
英文摘要	Tukey's halfspace median (HM), servicing as the multivariate counterpart of the univariate median, has been introduced and extensively studied in the literature. It is supposed and expected to preserve robustness property (the most outstanding property) of the univariate median. One of prevalent quantitative assessments of robustness is finite sample breakdown point (FSBP). Indeed, the FSBP of many multivariate medians have been identified, except for the most prevailing one-the Tukey's halfspace median. This paper presents a precise result on FSBP for Tukey's halfspace median. The result here depicts the complete prospect of the global robustness of HM in the finite sample practical scenario, revealing the dimension effect on the breakdown point robustness and complimenting the existing asymptotic breakdown point result.
资助项目	National Natural Science Foundation of China[11601197] ; National Natural Science Foundation of China[11461029] ; National Natural Science Foundation of China[71463020] ; National Natural Science Foundation of China[61263014] ; National Natural Science Foundation of China[61563018] ; National Natural Science Foundation of China[11171331] ; National Natural Science Foundation of China[11331011] ; National Science Foundation of Jiangxi Province[20161BAB201024] ; National Science Foundation of Jiangxi Province[20142BAB211014] ; National Science Foundation of Jiangxi Province[20143ACB21012] ; National Science Foundation of Jiangxi Province[20151BAB211016] ; Key Science Fund Project of Jiangxi Provincial Education Department[GJJ150439] ; Key Science Fund Project of Jiangxi Provincial Education Department[KJLD13033] ; Key Science Fund Project of Jiangxi Provincial Education Department[KJLD14034] ; National Science Fund for Distinguished Young Scholars in China[10725106] ; Key Lab of Random Complex Structure and Data Science, Chinese Academy of Sciences ; Natural Science Foundation of Shenzhen University
WOS研究方向	Mathematics
语种	英语
出版者	SCIENCE PRESS
WOS记录号	WOS:000400086700006
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/26033]
专题	应用数学研究所
通讯作者	Liu, XiaoHui
作者单位	1.Jiangxi Univ Finance & Econ, Sch Stat, Nanchang 330013, Jiangxi, Peoples R China 2.Jiangxi Univ Finance & Econ, Res Ctr Appl Stat, Nanchang 330013, Jiangxi, Peoples R China 3.Michigan State Univ, Dept Stat & Probabil, E Lansing, MI 48823 USA 4.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 5.Shenzhen Univ, Inst Stat Sci, Shenzhen 518006, Peoples R China
推荐引用方式 GB/T 7714	Liu, XiaoHui,Zuo, YiJun,Wang, QiHua. Finite sample breakdown point of Tukey's halfspace median[J]. SCIENCE CHINA-MATHEMATICS,2017,60(5):861-874.
APA	Liu, XiaoHui,Zuo, YiJun,&Wang, QiHua.(2017).Finite sample breakdown point of Tukey's halfspace median.SCIENCE CHINA-MATHEMATICS,60(5),861-874.
MLA	Liu, XiaoHui,et al."Finite sample breakdown point of Tukey's halfspace median".SCIENCE CHINA-MATHEMATICS 60.5(2017):861-874.