Ranks estimated from data are uncertain and this poses a challenge in many applications. However, estimated ranks are deterministic functions of estimated parameters, so the uncertainty in the ranks must be determined by the uncertainty in the parameter estimates. We give a complete characterization of this relationship in terms of the linear extensions of a partial order determined by interval estimates of the parameters of interest. We then use this relationship to give a set estimator for the overall ranking, use its size to measure the uncertainty in a ranking, and give efficient algorithms for several questions of interest. We show that our set estimator is a valid confidence set and describe its relationship to a joint confidence set for ranks recently proposed by Klein, Wright \& Wieczorek. We apply our methods to both simulated and real data and make them available through the R package rankUncertainty.

翻译：从数据中估计得出的排名具有不确定性，这给许多应用带来了挑战。然而，估计的排名是估计参数的确定性函数，因此排名中的不确定性必须由参数估计中的不确定性决定。我们以感兴趣参数的区间估计所确定的偏序的线性扩展为基础，给出了这种关系的完整刻画。然后，我们利用这种关系为整体排名提供了一个集合估计量，通过其大小来衡量排名中的不确定性，并针对若干感兴趣的问题给出了高效算法。我们证明了该集合估计量是一个有效的置信集，并描述了它与Klein, Wright & Wieczorek近期提出的排名联合置信集之间的关系。我们将我们的方法应用于模拟数据和真实数据，并通过R包rankUncertainty提供这些方法。