In this paper, we propose a new uncertainty set for robust models of linear optimization problems. We first study data-free and distribution-free statistical properties of continuous and independent random variables using the Probability Integral Transform. Based on these properties, we construct a new uncertainty set by placing constraints on the order statistics of random variables. We utilize the quantiles of random variables to depict the uncertainties and then adopt the formulation of the assignment problem to develop a tractable formulation for the order statistic uncertainty set. We show that the robust optimization models with the interval uncertainty set, the budget uncertainty set, and the demand uncertainty set can be obtained as special cases of the robust optimization model with the order statistic uncertainty set. Finally, using a robust portfolio construction problem as an example, we show via numerical experiments that the order statistic uncertainty set has better performance than other uncertainty sets when the sample size is small and the correlation between random variables is low.

在本文中，我们为线性优化问题的鲁棒模型提出了一个新的不确定性集。我们首先使用概率积分变换研究连续和独立随机变量的无数据和无分布统计特性。基于这些性质，我们通过对随机变量的阶统计量施加约束来构造新的不确定性集。我们利用随机变量的分位数来描述不确定性，然后采用分配问题的公式来开发顺序统计不确定性集的易于处理的公式。我们证明，作为具有阶次统计不确定性集的鲁棒优化模型的特例，可以获得具有区间不确定性集、预算不确定性集和需求不确定性集的鲁棒优化模型。最后，