A well-known result states that empirical quantiles for finitely distributed univariate random variables can be obtained by solving a linear program. We show in this short note that multivariate empirical quantiles can be obtained in a very similar way by solving a vector linear program. This connection provides a new approach for computing Tukey depth regions and more general cone quantile sets.

翻译：已知一个结果是，对于有限分布的一元随机变量，经验分位数可以通过解线性规划得到。我们在本文中展示，通过解向量线性规划可以类似地得到多元经验分位数。这一联系为计算*Tukey深度区域*和更一般的锥形分位集提供了一种新的方法。