论文标题
不可思议的比较：排名和选择为复合决策
Invidious Comparisons: Ranking and Selection as Compound Decisions
论文作者
论文摘要
有天生的人类趋势，人们可能将其称为“联盟桌上的心态”，以构建排名。学校，医院，运动队，电影和其他物体的排名也被排名，尽管它们固有的多维性表明 - 充其量只有部分订购才有可能。我们考虑了一大批基本排名问题，在这些问题中，我们观察到嘈杂的，对于潜在异质精度的$ n $对象的标量测量值，并被要求选择一组“最有功的对象”。这个问题自然是在罗宾斯（Robbins）（1956）的经验贝叶斯理论的复合决策框架中提出的，但它也与最近有关多重测试的文献有着密切的联系。混合模型的非参数最大似然估计器（Kiefer和Wolfowitz（1956））用于构建最佳排名和选择规则。在模拟和对美国肾脏透析中心排名的应用中评估规则的性能。
There is an innate human tendency, one might call it the "league table mentality," to construct rankings. Schools, hospitals, sports teams, movies, and myriad other objects are ranked even though their inherent multi-dimensionality would suggest that -- at best -- only partial orderings were possible. We consider a large class of elementary ranking problems in which we observe noisy, scalar measurements of merit for $n$ objects of potentially heterogeneous precision and are asked to select a group of the objects that are "most meritorious." The problem is naturally formulated in the compound decision framework of Robbins's (1956) empirical Bayes theory, but it also exhibits close connections to the recent literature on multiple testing. The nonparametric maximum likelihood estimator for mixture models (Kiefer and Wolfowitz (1956)) is employed to construct optimal ranking and selection rules. Performance of the rules is evaluated in simulations and an application to ranking U.S kidney dialysis centers.
