Invidious Comparisons: Ranking and Selection as Compound Decisions
研究了在观测到n个对象的含噪声标量测量值后，如何选出“最优”的一组对象。问题在Robbins的经验贝叶斯复合决策框架下自然形成，并采用非参数最大似然估计构建最优排名与选择规则，通过模拟和美国肾脏透析中心排名应用评估其表现。
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.