Ranks estimated from data are uncertain and this poses a challenge in many applications. The need to measure the uncertainty in sample ranks has been recognized for some time, but the previous literature considering this problem has been concentrated on measuring the uncertainty of individual ranks and not the joint uncertainty. We characterize the relationship between parameter uncertainty and rank uncertainty in terms of linear extensions of a partial order and use this characterization to propose a measure of the joint uncertainty in a sample ranking. We provide efficient algorithms for several questions of interest and also derive valid simultaneous confidence intervals for the individual ranks. We apply our methods to both simulated and real data and make them available through the R package rankUncertainty.

翻译：从数据中估计的等级是不确定的,这在许多应用中构成挑战。测量抽样等级的不确定性的必要性已经得到承认一段时间了,但以前研究这一问题的文献一直集中于衡量个别等级的不确定性,而不是共同的不确定性。我们从部分顺序线性扩展的角度来描述参数不确定性和等级不确定性之间的关系,并用这种特征来提出衡量抽样等级中共同不确定性的尺度。我们为若干感兴趣的问题提供有效的算法,并为个别等级提供有效的同时信任间隔。我们运用我们的方法模拟和真实的数据,并通过R包装单级Uncurety提供这些数据。