Invidious Comparisons: Ranking and Selection as Compound Decisions

• 成果类型: Article
• 署名作者: Gu, Jiaying; Koenker, Roger
• 署名单位: University of Toronto; University of London; University College London
• 刊物名称: ECONOMETRICA
• ISSN/ISSBN: 0012-9682
• DOI: 10.3982/ECTA19304
• 发表日期: 2023
• 页码: 1-41
• 关键词: false discovery rate; maximum-likelihood estimator; BAYES; impacts; ORACLE

摘要

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.