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arXiv · 1604.07104

The limit of finite sample breakdown point of Tukey's halfspace median for general data

Xiaohui Liu·Shihua Luo·Yijun Zuo
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Abstract

Under special conditions on data set and underlying distribution, the limit of finite sample breakdown point of Tukey's halfspace median ($\frac{1} {3}$) has been obtained in literature. In this paper, we establish the result under \emph{weaker assumption} imposed on underlying distribution (halfspace symmetry) and on data set (not necessary in general position). The representation of Tukey's sample depth regions for data set \emph{not necessary in general position} is also obtained, as a by-product of our derivation.

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Xiaohui Liu, Shihua Luo, Yijun Zuo. 2016-04-25. The limit of finite sample breakdown point of Tukey's halfspace median for general data. https://arxiv.org/abs/1604.07104

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