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：一个众所周知的结果表明，有限分布的单变量随机变量的经验分位数可通过求解线性规划获得。本文指出，多元经验分位数可通过求解向量线性规划以非常相似的方式获得。这一联系为计算Tukey深度区域及更一般的锥分位数集提供了新方法。