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.

翻译：人类有一种天生的倾向,人们可能会把它称为“ 工作桌心态 ”, 以构建排名。 学校、医院、体育队、电影和许多其他物体尽管其固有的多维性表明 -- -- 充其量只能是部分订购 -- -- 也只能是可能的。 我们考虑的是一大类初级排名问题,即我们观察到对可能具有不同精度的美元天体进行吵闹的、对优劣的量测,并被要求选择一组“最有价值的”天体。 这个问题自然地在Robbins的实验性贝耶斯理论(1956年)的复合决定框架中提出,但它也显示了与最近关于多次测试的文献的密切联系。 混合模型(Kiefer和Wolfowitz(1956年))的非对准最大可能性估测器被用于构建最佳的排位和选择规则。 规则的绩效在模拟中评估,并用于将美国肾脏透析中心排位。