摘要
Under special conditions on data set and underlying distribution, the limit of finite sample breakdown point of Tukey＇s halfspace median （1） has been obtained in the literature. In this paper, we establish the result under weaker assumptions imposed on underlying distribution （weak smoothness） and on data set （not necessary in general position）. The refined representation of Tukey＇s sample depth regions for data set not necessary in general position is also obtained, as a by-product of our derivation.
Under special conditions on data set and underlying distribution, the limit of finite sample breakdown point of Tukey＇s halfspace median （1） has been obtained in the literature. In this paper, we establish the result under weaker assumptions imposed on underlying distribution （weak smoothness） and on data set （not necessary in general position）. The refined representation of Tukey＇s sample depth regions for data set not necessary in general position is also obtained, as a by-product of our derivation.
基金
Supported by NSF of China(Grant Nos.11601197,11461029 and 61563018)
Ministry of Education Humanity Social Science Research Project of China(Grant No.15JYC910002)
China Postdoctoral Science Foundation Funded Project(Grant Nos.2016M600511 and 2017T100475)
NSF of Jiangxi Province(Grant Nos.20171ACB21030,20161BAB201024 and 20161ACB20009)
the Key Science Fund Project of Jiangxi Provincial Education Department(Grant Nos.GJJ150439,KJLD13033 and KJLD14034)
