Scatter halfspace depth is a statistical tool that allows one to quantify the fitness of a candidate covariance matrix with respect to the scatter structure of a probability distribution. The depth enables simultaneous robust estimation of location and scatter, and nonparametric inference on these. A handful of remarks on the definition and the properties of the scatter halfspace depth are provided. It is argued that the currently used notion of this depth is well suited especially for symmetric random vectors. The scatter halfspace depth closely relates to an appropriate distance of matrix-generated ellipsoids from an upper level set of the (location) halfspace depth function. Several modifications and extensions to the scatter halfspace depth are considered, with their theoretical properties outlined.

中文翻译：

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散布半空间深度：几何洞察

散布半空间深度是一种统计工具，它允许人们量化候选协方差矩阵相对于概率分布的散布结构的适应度。深度能够同时对位置和散射进行稳健估计，以及对这些进行非参数推断。提供了一些关于散射半空间深度的定义和属性的说明。有人认为，当前使用的这种深度的概念特别适合对称随机向量。散射半空间深度与矩阵生成的椭球距离（位置）半空间深度函数的上层集的适当距离密切相关。考虑了对散射半空间深度的几种修改和扩展，并概述了它们的理论特性。