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摘要翻译：
Tukey深度（也称为半空间深度）的计算非常苛刻，即使在低维空间也是如此，因为它需要考虑所有可能的一维投影。本文提出了一个近似于Tukey深度的随机深度。它只考虑了有限个随机选择的一维投影。因此，即使在高维空间中，这种随机深度也需要非常小的计算时间。而且，它很容易扩展以覆盖功能框架。我们给出了一些模拟，表明根据样本大小和样本空间的维数应该考虑多少个投影。我们还将此深度与文献中提出的其他一些深度进行了比较。值得注意的是，随机深度基于很少的投影数，得到了与其他深度非常相似的结果。
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英文标题：
《The random Tukey depth》
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作者：
J.A. Cuesta-Albertos and A. Nieto-Reyes
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最新提交年份：
2007
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分类信息：
一级分类：Statistics 统计学
二级分类：Computation 计算
分类描述：Algorithms, Simulation, Visualization
算法、模拟、可视化
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英文摘要：
The computation of the Tukey depth, also called halfspace depth, is very demanding, even in low dimensional spaces, because it requires the consideration of all possible one-dimensional projections. In this paper we propose a random depth which approximates the Tukey depth. It only takes into account a finite number of one-dimensional projections which are chosen at random. Thus, this random depth requires a very small computation time even in high dimensional spaces. Moreover, it is easily extended to cover the functional framework. We present some simulations indicating how many projections should be considered depending on the sample size and on the dimension of the sample space. We also compare this depth with some others proposed in the literature. It is noteworthy that the random depth, based on a very low number of projections, obtains results very similar to those obtained with other depths.
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PDF链接：
https://arxiv.org/pdf/707.0167
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